The resolution "expresses deep friendship toward the Scottish people" and "respects the right of the Scottish people to make their decision" on the issue on September 18.
It goes on to say: "The House of Representatives believes that a united, secure and prosperous United Kingdom is important for US national security priorities in Europe and around the world."
House Resolution 713 references Winston Churchill and the "special relationship" between the US and UK, and highlights the millions of Americans who have Scottish roots and ties.
It was introduced by Brad Sherman, Democratic congressman for San Fernando, California, on Monday and has attracted support from 27 Republicans and Democrats.
The resolution follows comments from Barack Obama, who previously observed that the UK appears to have ''worked pretty well''.
Speaking at a press conference with Prime Minister David Cameron in June, the US president said that America's interest in the referendum was to ensure it retained a ''strong, robust, united and effective" ally.
Commenting on the resolution, Sir Menzies Campbell, Liberal Democrat MP for North East Fife, said: "Notwithstanding the emotional connection with Scotland which many members of Congress have, there is no doubt that in both Senate and the House of Representatives there is concern at the idea of independence for Scotland and the impact that would have on the UK, which is regarded as one of America's closest allies and with whom we have a unique relationship in the sharing of intelligence.
"The names attached to this resolution and the positions they hold in the Congress makes it clear that this resolution is a serious expression of opinion.
"The signatories have rightly recognised that the decision is for Scottish people alone but following President Obama's previous intervention on this matter there can be no doubt about the level of American concern."
A spokesman for the pro-independence campaign Yes Scotland said: "It's great to know that Scotland has so many friends and admirers, and we know they will all continue to be our friends and admirers after we vote Yes on September 18.
"We're sure that everyone who genuinely has Scotland's interests at heart will be delighted in future years to see a fairer and more prosperous Scotland emerge using the great opportunities of independence to grow our economy and make an even bigger contribution on the global stage."