President Donald Trump and House Speaker Speaker Nancy Pelosi engaged in a political tit-for-tat over border wall funding this week, as the longest government shutdown in U.S. history seemed to have no end in sight. While the back and forth continues over border wall funding, the dubious claims mounted.

Welcome to Fact Check Friday.

Prayer rugs at the Southern border

On day 28 of the partial government shutdown, President Trump cited an article from a conservative news outlet reporting that residents along the Southern border have found Muslim prayer rugs. The president tried to use the story to show that people from outside of Mexico and Central America are illegally entering the U.S.

"Border rancher: “We’ve found prayer rugs out here. It’s unreal.” Washington Examiner," Trump tweeted. "People coming across the Southern Border from many countries, some of which would be a big surprise."

In his tweet, the president is falsely trying to tie prayer rugs used during worship by Muslims to terrorism and the threat of terrorists entering the United States via the Southern border.

There is no evidence of prayer mats being strewn across the border. The article the president referenced includes a list from Arizona's Customs and Border Protection of the countries of origins of people arrested on the border. None of those countries are predominantly Muslim.

In the last 5 days #YumaSector #BorderPatrol has arrested people from 7 countries trying to illegally enter the U.S. #NationalSecurity #SouthwestBorder

China

Guatemala

Honduras

Mexico

El Salvador

Nicaragua

India pic.twitter.com/8pHeFnbYOi

It's also the latest attempt by the president to bolster support for border security and justify his demands for $5.7 billion to build a wall or barrier, but, as we noted in last week's fact check, there is no evidence of terrorist operatives entering through Mexico, according to a State Department report.

“At year’s end there was no credible evidence indicating that international terrorist groups have established bases in Mexico, worked with Mexican drug cartels, or sent operatives via Mexico into the United States,” the department concluded in a 2017 report. “The U.S. southern border remains vulnerable to potential terrorist transit, although terrorist groups likely seek other means of trying to enter the United States.”

Administration officials, including Secretary of State Mike Pompeo and Department of Homeland Security Secretary Kirstjen Nielsen have repeatedly claimed that 3,755 "known or suspected terrorists were prevented from traveling to or entering the United States."

However, the Department of Homeland Security has clarified that the majority of these individuals were trying to come into the U.S. by air.

Giuliani: "I never said there was no collusion between the campaign!"

In an interview on CNN, President Trump's attorney Rudy Giuliani claimed he never said there was no collusion between the Trump campaign and Russia.

Giuliani was on CNN to defend his client, the president, regarding "false reporting" on the Russia investigation.

Chris Cuomo pressed Giuliani. "Mr. Mayor, false reporting is saying that nobody in the campaign had any contacts with Russia. False reporting is saying that there has been no suggestion of any kind of collusion between the campaign and any Russians."

"You just misstated my position," Giuliani jumped in to say. "I never said there was no collusion between the campaign! Or between the people in the campaign."

This simply isn’t true.

Giuliani, the president, and the White House, have claimed – at least a dozen times, according to an ABC News analysis – that there was no collusion between the Trump campaign and Russia.

According to sources close to Manafort defense: “The coooeration agree does not involve the Trump campaign....There was no collusion with Russia.” Another road travelled by Mueller. Same conclusion: no evidence of collusion President did nothing wrong. — Rudy Giuliani (@RudyGiuliani) September 15, 2018

After his appearance on CNN this week, Giuliani tried to clear up things up with a statement.

"I represent only President Trump not the Trump campaign," Giuliani said. "There was no collusion by President Trump in any way, shape or form. Likewise, I have no knowledge of any collusion by any of the thousands of people who worked on the campaign. The only knowledge I have in this regard is the collusion of the Clinton campaign with Russia which has so far been ignored."

President Trump claims on undocumented immigrant crime rates

President Donald Trump, speaking in New Orleans on Monday, listed tens of thousands of crimes he said were committed by undocumented immigrants, part of a pattern of statements he’s made linking immigrants to crime in his effort to gain support for his proposed border wall.

It echoed his prime-time address last Tuesday in which he used the same numbers.

Here’s the problem:

There is no national database that compares crimes committed by immigration status. In fact, only one state – Texas – does so. That means there’s no national database that breaks down crimes committed by native-born citizens or immigrants, or those in the country illegally, making it difficult to confirm or dispute the president’s numbers.

What available studies do show, however, is that overall, crime rates are lower among immigrant groups than they are among native-born Americans.

Read more from Cheyenne Haslett’s reporting.