Putin spoke Sunday at a gathering of the Shanghai Cooperation Organization (SCO) in Qingdao, China. He said that several countries, including Austria, have offered to host a Trump-Putin meeting.
The Russian leader said he shares concerns that Trump has voiced about a renewed arms race, adding that a thorough discussion is needed to address the issue.
Putin's remarks followed a report that White House officials were working toward setting up a meeting.
Trump has said he was open to having a summit with Putin, who U.S. intelligence officials have said directed Russian meddling in the 2016 election to help Trump win.
The U.S. leader has repeatedly said he wants to improve relationships with Moscow.
At the G-7 gathering in Canada on Friday, Trump suggested that Russia be offered a seat at the "negotiating table" of the organization, which was previously called the G-8 before Russia was ousted for annexing Crimea in 2014.
"We're looking for peace in the world,” Trump said Saturday, according to the Daily News. “We're not looking to play games."
During his Sunday remarks, Putin also addressed the situation in North Korea -- two days ahead President Trump's planned sit-down with North Korean leader Kim Jong Un in Singapore.
"Russia welcomes the planned summit of the U.S. and North Korea and notes China's big contribution to helping settle the crisis on the Korean Peninsula," Putin said. “We positively view the intentions of Pyongyang, Seoul and Washington to reach a comprehensive settlement of the crisis through talks."
Putin also criticized Trump's decision to exit the Iran nuclear deal, saying the withdrawal could “destabilize the situation” in the Middle East.
Trump pulled out of the 2015 Obama-era accord last month, despite objections from European allies and other nations.
Founded in 2001, the Beijing-based SCO has largely served as a vehicle for resolving border issues, fighting terrorism and — more implicitly — to counter American influence in Central Asia following its invasion of Afghanistan.
The location of the Sunday summit, Qingdao, China, is approximately 400 miles southeast of Beijing.