Donald Trump has insisted that the US military presence in Syria is “only for the oil”, contradicting his own officials who have insisted that the remaining forces were there to fight Isis.

Trump made his remarks while hosting Recep Tayyip Erdoğan, just over a month after the Turkish president launched an offensive into north-eastern Syria, which has been formally condemned as destabilising by state department officials.

Sitting alongside Erdoğan, Trump contradicted his own officials and the Republican leadership on a range of issues, most importantly on the US military mission in Syria. In a later press conference, the Trump declared himself a “big fan” of Erdoğan, and made no criticism of the Turkish incursion.

Erdoğan, however, criticised Trump for inviting a Kurdish leader he condemned as a terrorist to the White House. Erdoğan also noted he had returned a letter which Trump had sent to him on 9 October, urging his US counterpart to hold back his Syrian invasion plan.

“Don’t be a tough guy. Don’t be a fool!” Trump had said in the letter, which Erdoğan had said showed a “lack of respect”.

Asked about the letter on Wednesday, Erdoğan – through a translator – said: “We gave back the letter that we have received.”

Following Trump’s earlier insistence that his administration was solely interested in “keeping” Syrian oil, the US military deployed mechanised military units to oil fields in the east of the country.

However, seizing or benefiting from oil on a foreign territory, without permission from the sovereign authority, would be a violation of international law. Several US officials had sought to interpret the president’s remarks as meaning the US was denying Isis access to the oil.

“Our mission is the enduring defeat of Isis,” the defence secretary, Mark Esper, told reporters on Wednesday, adding: “We’re going to have about 500 to 600-ish troops there, at the end of the day.”

“A way that we ensure the enduring defeat of Isis is deny them access to the oilfields because if they have access to the oil fields, they can generate revenue. If they can generate revenue, then they can pay fighters, they can buy arms, they can conduct operations,” Esper said.

On the same day however, Trump repeated his intention that the US should take possession of the oil in the region.

“We’re keeping the oil. We have the oil. The oil is secure. We left troops behind only for the oil,” Trump said.

At a joint press conference with Erdogan, the US president said the ceasefire in north-east Syria “while complicated, is moving forward and moving forward at a very rapid clip”.

Erdoğan praised Trump, describing him as “a dear friend”, but went on to denounce the US partnership with Syrian Kurdish forces.

Both parties in Congress have condemned the Turkish incursion and threatened sanctions unless it is reversed. US officials have describe it as unwelcome and destabilising. In the run-up to Erdoğan’s controversial visit to Washington, senior officials expressed concern about reported war crimes committed by Turkish-backed Arab militias spearheading the offensive. One senior official told reporters that the US held Ankara responsible.

However, sitting alongside Erdoğan, Trump said: “I want to thank the president for the job they’ve done.”

“The president and I have been very good friends, we’ve been friends for a long time – almost from day one,” Trump said. “I understand the problems that they’ve had, including many people from Turkey being killed, in the area that we’re talking about.”

It is unclear what the president meant. Turks have not been killed in significant numbers in north-eastern Syria, nor is there evidence of attacks on Turkey being launched from the area.

There are strong links between the Kurdish People’s Protection units (YPG), the main force in the SDF, and the insurgent Kurdistan Workers’ party (PKK), which has carried out attacks inside Turkey.

In blunt remarks in the White House on Wednesday, Erdoğan criticised Trump for inviting the SDF leader Mazloum Kobani, (to whom he referred by his birth name, Ferhat Abdi Şahin) to the White House. Noting his PKK links, Erdoğan blamed Mazloum for hundreds of civilian deaths and said: “A person like this should not be welcomed by a country such as the United States.”

It is not the administration’s official position that PKK attacks justify the incursion into Syria. Officials including Jeffrey have criticised Turkey for abandoning a joint security mechanism agreed with the US, and invading the safe zone along the border that mechanism was intended to safeguard.

Challenged by a Turkish reporter about US links with the YPG despite its ties to the PKK, Trump said that the US had “a great relationship with the Kurds”, adding: “A lot of that is definition – what’s your definition of the various groups within the Kurds. You have various groups and some like them and some don’t.”

But he shrugged off the broader concerns voiced by administration officials and Republican leaders about the Turkish invasion.

“It’s time for us not to be worried about other people’s borders. I want to worry about our borders,” the president said.