EDINBURGH (Reuters) - Scotland will vote to remain in the European Union in a June 23 referendum, but support for a new independence vote is weak even if the country is pushed out of the EU by the vote in Britain as a whole, according to a poll published on Wednesday.

Support to remain in the EU stood at 51 percent in Scotland versus 21 percent for those backing a "Leave" vote, according to the TNS poll of around 1,000 people, a bigger margin to stay than seen for Britain as a whole.

Scots voted 55 to 45 percent against independence in September 2014. But the devolved nationalist government says it should have the right to hold a new vote if Scotland is forced out of the EU "against its will."

The survey found that 46 percent of Scots did not think the country should hold a new referendum, even if it votes to stay and the rest of the United Kingdom votes to leave, while 43 percent thought there should be a new consultation.

Support for independence per se was 38 percent while 48 percent backed sticking with the UK. The poll was carried out between May 4 and May 22.

Scotland has about 3.9 million registered voters, out of a total of 44.7 million across the UK's four constituent parts.

Britain's vote on whether to remain in the 28-member bloc has sweeping implications for the economy, trade, politics, defense and migration, as well as for the future of the EU itself.

TNS said it conducted all interviews for the poll face-to-face, in people's homes, using a computer-assisted personal interviewing technique.

(Reporting by Elisabeth O'Leary editing by Estelle Shirbon)