Broad majorities of Americans in a new ABC News/Washington Post poll support establishing diplomatic relations with Cuba, as well as ending the United States' longstanding trade embargo and restrictions on travel to and from the Caribbean nation.

Sixty-four percent favor Cuban-American diplomatic relations, similar to its level in polls the last eight years. Two-thirds and three-quarters, respectively, favor ending the trade embargo and travel restrictions, both up considerably from an ABC/Post poll in 2009.

See PDF with full results, charts and tables here.

No more than three in 10 are opposed in each case. And strong supporters outnumber strong opponents on all three measures - by particularly large margins, about 2-1, when it comes to trade and travel.

Barack Obama moved last week to normalize U.S. relations with Cuba, restoring diplomatic relations and further easing some trade and travel restrictions. This poll, produced for ABC by Langer Research Associates, indicates a solid base in public opinion for such initiatives.

Views on Cuba have transformed considerably over the years. In similar questions in 1998, just 38 percent supported diplomatic relations, only 35 percent wanted to end the embargo and Americans split evenly on doing away with the travel restrictions.

There are partisan and ideological gaps, but also some surprises. Even among Republicans and conservatives, majorities support ending the embargo and travel restrictions. They split evenly in the case of establishing diplomatic relations, with "strong" conservatives opposed. Support is much higher among Democrats, independents, liberals and moderates alike.

Among other groups, men, Hispanics, younger or middle-aged adults and higher-income earners, for the most part, are more apt than their counterparts to favor closer ties with Cuba.

METHODOLOGY - This ABC News/Washington Post poll was conducted by landline and cell phone Dec. 17-21, 2014, in English and Spanish, among a random national sample of 1,011 adults. Results have a margin of sampling error of 3.5 points. The survey was produced for ABC News by Langer Research Associates of New York, N.Y.