Speaking Wednesday night after meeting with Japanese Prime Minister Shinzo Abe in the Dutch port city of Rotterdam, Rutte said he and his European allies are striving "to help my British colleague to bring the vote next week to a successful outcome."
Rutte did not elaborate on what he and other leaders are doing to help win support for May's Brexit deal in the deeply divided British House of Commons. However Rutte stressed that "the present deal on the table is, I think, the best deal."
British lawmakers have dealt Prime Minister Theresa May her second defeat in two days in battles over the government's plans for Brexit.
The House of Commons voted for a motion designed to prevent the government delaying key decisions as Brexit approaches on March 29. The measure says that if Parliament rejects the divorce deal May has agreed with the European Union, the government must come up with a "Plan B" within three days.
The government previously had 21 days to report back to Parliament.
Lawmakers are due to vote on May's deal on Tuesday, and look likely to reject it.
Opponents of the agreement suspect the government may try to run down the clock, to leave Parliament facing a last-minute choice between May's deal and a no-deal Brexit.
On Tuesday, lawmakers voted to put curbs on the government's ability to spend taxes on no-deal measures.
A top European Parliament leader is appealing to lawmakers in London to show "responsibility" as they resume consideration of Britain's divorce deal with the European Union.
Many British lawmakers detest the deal agreed between Brussels and Prime Minister Theresa May. Britain is due to leave the EU March 29, and fears have risen that it may do so without a deal in place.
Manfred Weber, a German conservative who heads the biggest group in the European Parliament, said in Berlin Wednesday that "it's Britain's move. Our colleagues in Britain's lower house carry great responsibility now — the agreement is on the table."
News agency dpa reported that Weber said everyone must realize that a no-deal withdrawal on March 29 would "lead to very difficult, perhaps even chaotic situations."
The British government is bringing its little-loved Brexit deal back to Parliament, a month after postponing a vote on the agreement to stave off near-certain defeat.
Lawmakers are beginning five days of debate Wednesday on the agreement with the European Union setting out the terms of Britain's departure from the bloc on March 29.
A vote, initially slated for December, is scheduled for Jan. 15.
But opposition remains strong from both pro-Brexit and pro-EU U.K. lawmakers. Brexiteers are urging the government to ramp up preparations for leaving the EU without a deal.
But many lawmakers, and businesses, say that could cause economic turmoil.
The de-facto deputy Prime Minister, David Lidington, said the only way to avoid a disruptive no-deal "is for Parliament to endorse and ratify a deal."