STOCKHOLM (Reuters) - Social Democrat Prime Minister Stefan Lofven is Swedish voter's most trusted leader, a poll showed on Thursday, despite a crisis that saw parliament pass a vote of no-confidence in him at the start of the week.

       The Novus poll showed 38% of Swedes have confidence in Lofven, ahead of his most likely rival for the post of prime minister, centre-right Moderate Party leader Ulf Kristersson, who was backed by 35% of voters.

       Lofven has a week to resign or call a new election as a result of Monday's no-confidence vote and the former welder is in last-ditch talks to keep his minority coalition in power.

       Lofven needs to persuade the Left Party - whose decision to withdraw support from the government triggered the crisis - and the Liberal Party to back him in order to form a viable government.

       The Left Party could come back on board, after changes to plans to ease rent controls - the issue that caused them to turn their back on Lofven.

       The Liberals have said they want Kristersson as prime minister, but the centre-right Moderate leader cannot command a majority in parliament and a snap election is looking increasingly likely.

       Opinion polls show the Liberals could drop below the 4% threshold to get seats in parliament, putting pressure on them to do a deal with Lofven.

       The Novus poll showed Lofven's support had risen 2% since March with Moderate leader Ulf Kristersson's falling 1%.

       Among the other gainers were Jimmie Akesson, head of the nationalist Sweden Democrats - the party which called the vote of no-confidence in Lofven - and Left Party leader Nooshi Dadgostar. Liberal leader Nyamko Sabuni was also more popular.

       (Reporting by Simon Johnson; Editing by Angus MacSwan)