TRUMP, on Montana Democratic Sen. Jon Tester: "Tester joined every other Senate Democrat in supporting open-border legislation from the now-legendary Dianne Feinstein." — Montana rally Saturday.

APTOPIX Election 2018 Trump

President Donald Trump arrives for a campaign rally at Bozeman Yellowstone International Airport, Saturday, Nov. 3, 2018, in Belgrade, Mont. (AP Photo/Evan Vucci)

THE FACTS: He's misrepresenting a bill that does not direct borders to be more porous than now.

Democratic Sen. Dianne Feinstein of California is sponsoring a bill that has the support of every Democratic senator including Tester. The bill's aim is to stop the Trump administration's "zero tolerance" policy of criminally prosecuting all adults caught crossing the border illegally and putting their children under Department of Health and Human Services custody and care.

The bill seeks to limit family separations by barring federal agents and officers from removing a child from a parent within 100 miles of U.S. borders. Exceptions would apply in cases where a child is danger of trafficking or abuse or neglect, or when there is a strong likelihood the adult is not the parent.

While Trump asserts that the bill would spur "open borders" and change immigration law, nothing in the legislation would prohibit the removal or detention of immigrants who arrive in the U.S. illegally if the families are kept together.

TRUMP, on the practice of allowing immigrants caught crossing the border illegally to stay in U.S. communities as they await immigration hearings: "We're not doing releases. What's been happening over years is they would come in, release them, and they would never show up for their trial. And we now have 25 or 30 million people in this country illegally, because of what's been happening over many years." — remarks Wednesday to reporters.

THE FACTS: It's nowhere close to 25 million to 30 million, nor has the number increased much in recent years.

The nonpartisan Pew Research Center estimates there were 11.3 million immigrants in the U.S. illegally in 2016, the most recent data available. That number is basically unchanged from 2009. Advocacy groups on both sides of the immigration issue have similar estimates.

The number of such immigrants had reached a height of 12.2 million in 2007, representing about 4 percent of the U.S. population, before declining due in part to a weakening U.S. economy.

TRUMP, on tweeting a video blaming Democrats allowing a man to enter the U.S. who killed two police officers: "All I'm doing is just telling the truth." — speaking to reporters Friday.

APTOPIX Election 2018 Trump

President Donald Trump waves off a reporters question as he speaks to members of the media on the South Lawn before boarding Marine One at the White House in Washington, Friday, Nov. 2, 2018, for a short trip to Andrews Air Force Base, Md., and then on to Huntington, W.Va., and Indianapolis for campaign rallies. (AP Photo/Andrew Harnik)

THE FACTS: The video he spread around does not tell the truth. It says Democrats let Luis Bracamontes into the country and "let him stay."

Bracamontes entered the U.S. illegally, in 1996, during the Democratic administration of President Bill Clinton, but he was also deported by that administration the next year after being caught buying crack cocaine and serving his sentence. He returned repeatedly. By the time he was sentenced to death in California for the 2014 killings of the police officers, he had been deported four times, according to Sacramento County Sheriff Scott Jones.

No evidence of leniency by Democrats has emerged in the episode. Democratic and Republican administrations alike have deported hundreds of thousands of people a year and no administration, Trump's included, has caught everyone trying to enter illegally.

TRUMP on what U.S. troops should do if encountering migrants who are trying to get to the border from Mexico: "I didn't say shoot, I didn't say shoot." — remarks to reporters Friday.

THE FACTS: A day earlier, he said of the migrants: "They want to throw rocks at our military, our military fights back. I told them, consider it a rifle."

The procession has been largely peaceful. Some migrants in one caravan clashed with Mexican police at the Mexico-Guatemala border, hurling stones.

TRUMP: "President Obama separated the children from parents and nobody complained. When we continued the exact same law, the country went crazy." — immigration speech Thursday.

Trump Immigration

President Donald Trump talks about immigration and gives an update on border security from the Roosevelt Room of the White House in Washington, Thursday, Nov. 1, 2018. Trump says asylum seekers must go to ports of entry in order to make a claim. He says he will issue an executive order next week on immigration. (AP Photo/Susan Walsh)

THE FACTS: Actually, Obama did not do the same thing as a matter of policy.

While it's true the underlying laws were the same, the Trump administration mandated anyone caught crossing the border illegally was to be criminally prosecuted. That policy meant adults were taken to court for criminal proceedings, and their children were separated and sent into the care of the Health and Human Services Department, which is tasked with caring for unaccompanied migrant children. Trump's zero tolerance policy remains in effect, but he signed an executive order June 20 that stopped separations.

Jeh Johnson, Obama's Homeland Security secretary, recently told NPR there may have been unusual or emergency circumstances when children were taken from parents, but there was no such policy.

TRUMP: "At this very moment, large well-organized caravans of migrants are marching towards our southern border. Some people call it an invasion. ...These are tough people in many cases; a lot of young men, strong men and a lot of men that maybe we don't want in our country. ...This isn't an innocent group of people. It's a large number of people that are tough. They have injured, they have attacked." — immigration speech Thursday.

Central America Migrant Caravan

Central American migrants, part of the caravan hoping to reach the U.S. border, get a ride on a truck in Donaji, Oaxaca state, Mexico, Friday, Nov. 2, 2018. The migrants had already made a grueling 40-mile (65-kilometer) trek from Juchitan, Oaxaca, on Thursday, after they failed to get the bus transportation they had hoped for. But hitching rides allowed them to get to Donaji early, and some headed on to a town even further north, Sayula. (AP Photo/Rodrigo Abd)

THE FACTS: He's given no evidence that people in the caravans are, by and large, dangerous, hardened criminals — after acknowledging at one point that there is no such proof.

The migrants in the caravans are mostly from Honduras, where it started, as well as El Salvador and Guatemala. Overall, they are poor, carrying the belongings that fit into a knapsack and fleeing gang violence or poverty.

It might be true there are some criminals mixed in with the throngs, given the sheer number of migrants. Trump did not substantiate his claim that members of the MS-13 gang, in particular, are among them. The Homeland Security Department issued a sheet stating that "over 270 individuals along the caravan route have criminal histories, including known gang membership." But it did not specify how it had arrived at that number.

Some migrants in one of the caravans clashed with Mexican police at the Mexico-Guatemala border, hurling stones and other objects as they tried to cross the international bridge. One migrant died; it's not clear how it happened. Caravan leaders said they had expelled a number of troublemakers from the procession, exhibiting some self-policing. Ultimately, most entered Guatemala — and later, Mexico — by illegally bypassing immigration checkpoints.

The caravan otherwise has been overwhelmingly peaceful, receiving applause and donated food from residents of the towns they pass. Mexican police have not tried again to stop them.