But Trump has consistently resisted the suggestion that he confront Putin over the matter, saying Putin has repeatedly denied involvement.
President Trump has said he "had not thought" about asking Mr Putin to extradite the dozen Russians but said that "certainly" he would "be asking about it". So having meetings with Russia, China, North Korea, I believe in it.
Trump had said at a Friday joint press conference with May that he had provided a suggestion to her about handing Brexit negotiations, and that she had not taken it.
During the 2016 campaign, Trump had publicly encouraged Moscow to hack Clinton's emails, saying at an event: "Russia, if you're listening, I hope you're able to find the 30,000 emails that are missing", a reference to Clinton's controversial use of private, non-governmental email server while she was U.S. secretary of state.
"Well, I think we have a lot of foes". But again, this was during the Obama administration.
The meeting came in the midst of tensions between Russian Federation and the West in issues concerning Iran, Syria and Crimea, as well as the unprecedented alienation between the United States and its trans-Atlantic allies over trade and defense.
Mueller is investigating possible collusion between Trump's campaign and Russian Federation.
"Of course not. Really, honestly, Jonathan, I think the question's silly", he said.
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"Nothing bad is going to come out of it, and maybe some good will come out", he said.
"I think the European Union is a foe, what they do to us in trade", Trump said on CBS' "Face the Nation" on Sunday.
They are accused of using keystroke reading software to spy on the chair of the Democratic National Committee (DNC) and hack into the party's computers.
The indictment, which alleges a wide-ranging conspiracy involving sophisticated hacking and staged releases of documents, raises the stakes for a summit next week between President Trump and Russian President Vladimir Putin.
"It doesn't feel good to have them here", said Anna Bruun, a civil servant who said she was opposed to "great power politics" playing out in her home city.
After that suggestion was rebuffed by the White House, the Democrats said Trump should at least ensure his national security team is alongside him with Putin at all times, "not wing it on your own".
Mr Trump is due to meet Mr Putin in the Finnish capital Helsinki.
"We consider Trump a negotiating partner", said Kremlin adviser Yuri Ushakov.
"I can't tell you what's going to happen, but I can tell you what I'll be asking for".
Trump also defended his decision to hold the meeting after coming under fire from opposition Democrats in the wake of the indictments. "We can do more, so if you want to do an arms race you'll lose", according to the report. "An interference by the US Congress is probable; it has repeatedly shown its desire to limit the powers of the US president in matters relating to Russian Federation", he said.