Trump says the country has "historically been a funder of terrorism at a very high level".
"We will continue to give all our support to Qatar", Recep Tayyip Erdogan said at an iftar (fast-breaking meal) with members of his Justice and Development (AK) Party in Istanbul.
But US officials insisted that both men were sending the same message that the countries of the region should not allow their differences to hinder the fight against extremism.
Earlier this week, Saudi Arabia, the United Arab Emirates, Egypt and Bahrain unleashed a raft of punitive measures against Qatar, severing diplomatic ties and accusing it of supporting terrorism in the region.
"The blockade is hindering USA military actions in the region and the campaign against ISIS", Tillerson said, without providing details.
Kuwait has led a regional effort to mediate, but the four states intensified the pressure on Friday by placing dozens of people with alleged links to Qatar on terrorism blacklists.
Tillerson phoned Saudi Deputy Crown Prince Mohammad Bin Salman on Sunday and the two discussed efforts to combat terrorism and "funding of terrorist organizations in a bid to achieve security and stability in the region", state-run Saudi Press Agency reported.
Saudi Arabia, United Arab Emirates, Bahrain and Egypt on Monday snapped diplomatic relations with Qatar.
More than a third of the world's liquefied natural gas trade comes from Qatar, making it the world's largest producer and exporter of LNG.
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman bin Jassim Al-Thani speaks with Russian Foreign Minister Sergey Lavrov, right back to the camera, during their meeting in Moscow, Russia, Saturday, June 10, 2017. Also named were Doha-based Muslim Brotherhood spiritual leader Yusuf al-Qaradawi and Qatari-funded charities. Countries across the world - including Japan, China, Pakistan, the U.K., France, Turkey, Brazil and Argentina - rely on the state-run corporation for much of their energy needs.
Qatar Airways also stopped its flights to the four Arab countries in response to the UAE's Etihad, Emirates, FlyDubai, EgyptAir and Bahrain's Gulf Air suspending flights to Qatar. "We have to stop the funding of terrorism. the time had come to call on Qatar to end its funding they have to end that funding and its extremist ideology in terms of funding", said the US President. The Arab states have also ordered Qataris out within 14 days.