* Government circulates letter to FTSE 100 companies
* Public letter backs government's Brexit strategy
* Several companies reluctant to commit (Adds reaction from opposition Labour Party)
LONDON, Sept 6 (Reuters) - The British government has asked FTSE 100 companies to sign a public letter endorsing its Brexit strategy, four sources familiar with the matter said on Wednesday, risking further strains with firms who are reluctant to agree.
Britain's vote last year to leave the European Union has damaged relations between major companies and the government, with businesses increasingly concerned that moves to leave the single market and customs union would damage their operations.
On Wednesday, many were alarmed at a leaked government report that set out plans to curb immigration for lower skilled workers while others have complained that they have little visibility of how Brexit will unfold.
"We believe this is a good time for employers to work with government and parliament to make a success of Brexit and secure a bright future for our country," said the letter, circulated to FTSE 100 companies.
A spokesman for Prime Minister Theresa May declined to comment but said there had been lots of engagement with companies over Brexit.
It is not the first time a government has asked big business to lend its support, with high profile figures previously signing letters published in national newspapers that backed the policies of former prime minister David Cameron.
"We welcome the government's commitment to negotiating an interim period so that firms can ensure they are ready to adapt to the changing relationships and thrive under the new partnership being created with the EU," it adds.
One source said the Brexit letter was received last Thursday and said the government hoped to publish it as early as this Thursday. The source, who said they had not decided whether to sign, added that the contents often change as companies agree to comply.
Another source said they had also read the letter.
Two other sources said they were reluctant to commit.
"This certainly raised a few eyebrows," a FTSE 100 executive, who is in regular talks with the government, told Reuters. "We are very reluctant to be dragged into politics at the best of times. Right now we don't want to endorse a plan that is going to do enormous damage to our industry.
The second source said they had "no appetite to sign".
Jonathan Reynolds, City spokesman for the opposition Labour Party, described the government as "desperately trying to canvass support" for its Brexit negotiations.
"It's telling and alarming that business leaders have so little confidence in this governments approach that they are reluctant to sign even this lukewarm statement," he said. (Additional reporting by Kylie MacLellan; Editing by Alison Williams)