Ambassador Nikki Haley said Trump had gone into the meeting "to basically look him in the eye, let him know that, yes, we know you did it and cut it out."
But she declined to say what penalties Moscow might face for such meddling.
The US and Russian sides have issued sharply conflicting accounts of the meeting yesterday in Hamburg, Germany between the two leaders. Russia has denied meddling, and Putin said today that in the meeting, "I got the impression that my answers satisfied him" and that Trump "agreed."
Questioned at a news conference about the differing view of the meeting described by Trump's advisers, Putin told reporters that "you should ask him."
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But Trump -- breaking with normal practice by US presidents and many other leaders at the end of a G20 meeting -- left Hamburg without holding a news conference.
The first face-to-face meeting between Trump and Putin had aroused exceptional interest, amid ongoing investigations into contacts between members of Trump's presidential campaign and Russian officials.
"Any country needs to know that there are consequences when they get involved in our elections," Haley told CNN. "And I think that's why it's good that the investigations are going on."
But asked what specific consequences Russia might face following the meeting yesterday, she replied, "I think you're going to have to ask the president.
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