The plan, which may be included in his State of the Union address next week, is to help low-income couples with their interpersonal skills and publicise the value of marriage.
"This is a way for the president to address the concerns of conservatives and to solidify his conservative base," a presidential adviser told the New York Times.
A year of rulings on same-sex relationships could make gay rights the touchstone issue in the forthcoming election. In June the supreme court declared the anti-sodomy laws applied by some states unconstitutional, effectively making consensual sex between gay couples legal.
In November Massachusetts became the first state to legalise gay marriage, ruling that it was unconstitutional to deny the right to gay couples. The ordination of the Episcopal church's first openly gay bishop kept the issue centre stage.
Mr Bush is under pressure to denounce gay marriage and amend the constitution to enshrine marriage as exclusively the bond between man and woman. But he has held back for fear of alienating moderate Republicans and independent voters.
He has said that he would support an amendment if necessary, but that he was happy for states to make their own arrangements.
A New York Times poll last month showed that 61% were opposed to gay marriage and 34% in favour; 55% favoured a constitutional amendment and 40% opposed it.
Avoiding the words "heterosexual marriage", administration officials are referring to "healthy" marriages.
"Marriage programmes do work," Wade Horn, the assistant secretary of health and human services for children and families, said. "On average children raised by their own parents in healthy, stable married families enjoy better physical and mental health and are less likely to be poor."
The programme will focus on young adults interested in marriage, secondary school students and unmarried couples who have just had children, according to federal officials. Mr Bush is likely to ally himself personally to the initiative by visiting poor areas where marriage rates are low.
"The president loves to do that sort of thing in the inner city with black churches, and he's very good at it," an aide said.
The plan has been criticised as invasive and counter-productive.
"Such programmes intrude on personal privacy, may ignore the risk of domestic violence and may coerce women to marry," said Timothy Casey, a lawyer for the National Organisation of Women.
Some conservative groups believe the proposals do not go far enough.
"We have a hard time understanding why the reserve," said Glenn Stanton, a policy analyst at the conservative Christian organisation Focus on the Family.
"You see him inching in the right direction. But the question for us is, why this inching. Why not just get there?"