In a press conference a few hours before Pompeo's arrival, Abdel Mahdi said Iraq would not accept any attack on foreign troops on its land.
An Iraqi government source confirmed the meeting with Abdul Mahdi but did not elaborate on the details, Reuters reported.
Mr Pompeo warned earlier this year that the United States will not "partner" with countries that adopt Huawei systems.
US officials have said there are indications Iran is planning to retaliate for the Trump administration's stepped-up sanctions on the country, although the threat information remains vague.
U.S. Secretary of State Mike Pompeo made a lightning visit to Baghdad on Tuesday to show U.S. support for the Iraqi government as Washington steps up warnings to Iran against any action against American interests in the Middle East.
The Trump administration has imposed sweeping sanctions on Iran, including trying to stop all exports of its oil, although it has issued a waiver for energy-starved Iraq to keep buying power from its neighbour.The deployment of the USS Abraham Lincoln was announced on Sunday. The US military said on Tuesday B-52 bombers would be part of additional forces being sent to the Middle East to counter what the administration of US President Donald Trump says is "clear indications" of threats from Iran to US forces there.
Pressure on May to set timetable for departure intensifies
Why?" Leaders of local Conservative organisations are holding a non-binding no-confidence vote in May's leadership on June 15. But the Telegraph is now saying that Theresa May is planning three major concession as a basis for a deal with Labour.
Markets Right Now: Stocks sink as tariff deadline approaches
Nonetheless primarily the most fresh hard talk is raising panic on Wall Boulevard and casting extra doubt about a resolution. Chipmaker shares were also pressured by an underwhelming profit growth forecast from Intel Corp.
Meghan Markle's Father Wishes Family Well After Royal Birth
Royal fans will be hopeful that the royal baby's name will be revealed today around the time the photos are released. The siblings of Prince Harry's late mother Diana had also been told of the birth, it said.
Pompeo on Thursday canceled his scheduled visit to Greenland due to the escalation of tensions with Iran, media reported, citing a state department official.
Companies from signatory nations have been wary of investing in Iran for fear of triggering USA retaliation, leaving Tehran feeling that it has not reaped expected benefits from the deal in terms of access to finance and markets for its oil.
Iranian Foreign Minister Mohammad Javad Zarif dismissed such accusations. "Other than that, I just can't say any more". But it's not been through any deliberate fault of European partners. Iraq and Iran are neighbors, and maintain cordial relations. "It's beyond the control of governments to change that".
Late Sunday the administration announced that it is deploying a USA aircraft carrier and Air Force bombers to the Persian Gulf region.
Washington has ramped up sanctions on Tehran over its nuclear program in recent months and designated the Iranian Revolutionary Guard Corps as a terrorist group.
Trump withdrew from the Obama administration's landmark nuclear deal with Iran in May 2018 and, in the months that followed, reinstated punishing sanctions, including those targeting Iran's oil, shipping and banking sectors.