"This doesn't exactly look like an exchange of pleasantries between Theresa May and Jean-Claude Juncker as the Brexit summit gets underway", wrote journalist Philip Sime, sharing the video on Twitter.
Mr Juncker said he had been able to convince her that his remarks had referred to the wider Brexit debate in the United Kingdom, joking: "After having checked what I said yesterday night, she was kissing me".
"There is a majority in my Parliament who want to leave with a deal, so with the right assurances this deal can be passed", May said, warning her European Union counterparts that failure could mean Britain crashing out of the bloc without a deal, "with all the disruption that would bring". They held out little hope of offering any legal assurances that would help her sell a contentious withdrawal agreement to an unenthusiastic House of Commons.
Ms Rudd opposed Brexit in the 2016 referendum, and was reported by The Times newspaper to be among five cabinet ministers discussing whether another referendum is necessary if Mrs May's deal fails.
Theresa May went to Brussels seeking a way to get the Withdrawal Agreement through a heavily divided Commons, insisting she could do it but had to be able to convince MPs the United Kingdom would not find itself tied to the European Union indefinitely through the Northern Ireland "backstop".
"In the course of the morning after having checked what I said yesterday night, she was kissing me", he said.
"And what came out of that was his clarity that actually he'd been talking - when he used that particular phrase - he'd been talking about a general level of debate".
Her week from hell began Monday, when she scrapped a planned vote in Parliament on her Brexit divorce deal at the last minute to avoid a heavy defeat.
"I believe it is better to leave with a deal and a good deal", the PM said.
The transition was reached to avoid customs checks on the border separating Northern Ireland and the Irish Republic, but British lawmakers fear the European Union will string out negotiations for years and that Britain could be trapped indefinitely in the transition.
As he closed a summit in Brussels, the European council president took aim at treatment meted out to Theresa May, who faced a challenge to her leadership on the eve of the leaders' meeting.
Having survived a drubbing at home and overseas over the state of Brexit negotiations, May took issue with Juncker's view of Thursday's discussions.
He added: "We have to bring down the temperature".
"Negotiations like this are always tough", May said.
"Our UK friends need to say what they want, instead of asking us to say what we want", he said.
Labour's Brexit spokesman Keir Starmer, meanwhile, has called for May to move on and put the deal to MPs.