Theresa May held talks at 10 Downing Street with the president of the European Parliament over MEPs' red lines for Brexit negotiations.
The parliament earlier this month agreed a hard-line negotiating position which included demands for the UK to meet its financial obligations to the EU in full and delay talks on trade until after a divorce settlement is reached.
Any deal secured by Mrs May under Article 50 of the EU treaties must be approved by MEPs in a vote at the end of the two-year process, giving the European Parliament an effective veto.
The Prime Minister greeted Antonio Tajani with a handshake on the doorstep of Number 10, but the pair made no comment to waiting reporters.
Mr Tajani last week said his priority for Brexit was "defending the rights of our citizens" affected by the UK's decision to withdraw from the EU.
The Prime Minister received a Brexit boost on Wednesday, with US House of Representatives speaker Paul Ryan saying the US stands ready to strike a free trade deal with the UK as soon as possible.
Leaving Downing Street after talks lasting 45 minutes, Mr Tajani said he and Mrs May were agreed on the need for a resolution to the issue of UK and EU ex-pats' rights.
He said: "The message is a positive message. We want to strengthen the citizens' rights - European citizens living in the UK and UK citizens living in the European Union.
"This is the most important message - we want to work together.
"Mrs May underlined this position. It is our position. Here we were both in favour of our citizens.
"It is a good start, a good beginning; now we need to go for implementation."