Donald Trump had a “very good” conversation with Vladimir Putin, the Russian president, about a diplomatic resolution to the Syrian civil war, including the creation of safe zones, the White House said on Tuesday.

The two leaders held their first known phone discussion since last month’s US missile strikes against a Syrian government airbase soured relations between Washington and Moscow.

“President Trump and President Putin agreed that the suffering in Syria has gone on for far too long and that all parties must do all they can to end the violence,” a White House statement said. “The conversation was a very good one, and included the discussion of safe, or de-escalation, zones to achieve lasting peace for humanitarian and many other reasons.”

The US said it would be sending a representative to ceasefire talks in Astana, the capital of Kazakhstan, on Wednesday. Trump and Putin also discussed cooperation to “eradicate terrorism” throughout the Middle East and how best to resolve the “very dangerous” situation in North Korea.

A Kremlin readout of the phone call said Trump and Putin had focused on the “possibility of coordinating Russian and US actions for the fight against international terrorism in the context of the Syria crisis” and agreed to work to establish a real ceasefire there.

As for North Korea, Putin called for “restraint and lowering the level of tension” on the Korean peninsula.

The readout also laid a timeline for the long awaited face-to-face meeting between Trump and Putin, who had voiced admiration for each other before tensions rose last month.

The two leaders “spoke out … in favour of organising a personal meeting in connection with the session of the Group of 20 summit in Hamburg on 7-8 July”.

Putin’s spokesman previously suggested the pair could meet on the sidelines of the summit, but there had been no concrete agreement on this.

Trump faced domestic criticism over what he did not talk about in Tuesday’s phone call. Adrienne Watson, the deputy communications director of the Democratic National Committee, said: “Trump’s bromance with Putin appears to be back on track. Instead of sending Putin a tough message on backing Assad’s brutal regime, Trump appears to be opting for a strategy of appeasement.

“Just days ago, Trump once again cast doubt on whether Russia attacked our democracy. With no apparent talk of Russia’s abysmal record on human rights, no clear message on Assad’s future in Syria, and no condemnation of Russia’s continued aggression in Ukraine, it’s clear that ultimately, Putin is getting what he wants from Trump.”

The US president is already facing criticism for expressing admiration for authoritarian figures. He has praised Abdel Fattah el-Sisi of Egypt, congratulated Recep Tayyip Erdoğan of Turkey on a controversial referendum win, described North Korea’s Kim Jong-un as a “pretty smart cookie” and invited Rodrigo Duterte of the Philippines to the White House.

Trump and Putin have spoken twice since the US president took office in January, including early last month following an attack in St Petersburg.

But the relationship suffered a setback when Trump ordered missile strikes against Syrian government targets in early April after the regime used chemical weapons in a deadly attack on civilians. Russia condemned the intervention.

Trump – who spent months saying he hoped to “get along” with Putin – declared that relations between America and Russia “may be at an all-time low”. Tillerson and the UN ambassador, Nikki Haley, also spoke out against Moscow’s role in supporting Syria’s president, Bashar Assad.

Days later, however, Trump expressed hope on Twitter that “things will work out fine” with Russia and “everyone will come to their senses”.

The FBI and two congressional committees are investigating whether Trump’s campaign coordinated with Russia as it meddled in last year’s presidential election. Trump has vigorously denied any improper ties to Moscow, calling the Russian investigations a “hoax”.

Over the weekend he retreated from his earlier acceptance of the intelligence community’s finding that Russia was responsible for hacking senior Democrats’ emails.

Asked whether he believed that Russians tried to meddle in the election, he told CBS’s Face the Nation: “That, I don’t know. I don’t know.” The president said “it’s very hard” to say who was behind a hack without catching the hacker “in the act”.

“With that being said, I’ll go along with Russia,” Trump said. “Could’ve been China, could’ve been a lot of different groups.”

Meanwhile, two US Senators known for their tough stand on Russia have urged their colleagues to enforce comprehensive sanctions in response to its involvement in the election. John McCain of Arizona and Lindsey Graham of South Carolina said in a joint statement: “Now is not the time to send a signal to Russia that all is forgotten or forgiven.”