(Jae C. Hong/AP)

A record-high 6 in 10 Americans support same-sex marriage and a similar share say individual states should not be allowed to define marriage as only between a man and a woman, according to a new Washington Post-ABC News poll.

The national debate on same-sex marriage moves to center stage next week, when the Supreme Court hears oral arguments on whether state restrictions on same-sex marriage are unconstitutional.

Courts across the country have agreed with gay-marriage advocates that a Supreme Court ruling in 2013, striking down the federal government’s refusal to recognize legal same-sex unions, means that state restrictions must fall as well.

Next week, the court will be considering whether the Constitution requires that gay couples be allowed to marry and whether states may refuse to recognize same-sex marriages performed outside their borders.

Same-sex marriage status in the U.S., state-by-state

The rapid change in the law tracks a decisive rise in support for allowing gay couples to marry. It is driven by widespread support from younger generations as well as shifting attitudes among their elders.

The Post-ABC poll finds 61 percent of Americans support allowing gays to marry and 35 percent are opposed. Support is up only slightly from last year but is a reversal from public sentiment a decade ago, when opponents outnumbered supporters 58 percent to 39 percent.

In the short and long run, support for same-sex marriage has grown significantly across demographic and political groups.

Among those under age 30, support has grown since 2005 from 57 percent to 78 percent. Among those 65 and over, it has increased from 18 percent to 46 percent. Support has also risen by double digits across partisan groups, though Democrats and independents have shifted the most.

Despite that, wide swaths of opposition persist among important voting groups. More than 6 in 10 Republicans oppose allowing gay couples to marry, and that increases to 71 percent of conservative Republicans, who play a critical role in the party’s presidential primaries and caucuses.

Nearly half of seniors continue to oppose same-sex marriage. Other surveys find opposition among majorities of white evangelical Protestants and those who attend religious services at least once a week.

By contrast, the Post-ABC poll finds that majorities of Democrats, independents and every age group under 65 support allowing same-sex marriages.

There are 37 states, plus the District of Columbia, where, through the legislative process or court order, gay couples are allowed to marry. In those place, 64 percent say such unions should be legal. But even in the 13 states where same-sex marriage is not legal, 54 percent say it should be.

The public’s perspective on whether states may forbid same-sex marriage mirrors overall views on the subject, according to the poll. Sixty-one percent oppose allowing states to prohibit same-sex marriages, and 62 percent support requiring states to recognize same-sex marriages performed in other states.

Intensity of opinion also favors same-sex marriage supporters. At least 4 in 10 “strongly” back gay marriage, support requiring states to recognize out-of-state gay marriages and oppose statewide prohibitions.

While numerous public polls have found growing support for gay marriage in recent years, findings about whether the right should be available nationwide or whether states may decide have been less consistent across different question wordings.

For instance, a February CBS News poll found a 56 percent majority saying individual states should be allowed to determine whether same-sex marriage is offered. However, an Associated Press-GfK survey in late January and early February found the public evenly split on whether the Supreme Court should rule same-sex marriage legal nationwide.

Surveys have found that opinions on legal questions are tied closely to support for same-sex marriage itself. In recent years, those who support allowing gay unions have been more favorable toward a national approach, while opponents have favored autonomy for states.

Reactions to the Supreme Court’s decision, which is likely to come in June, may also be guided by core support for same-sex marriage, as they have in the past. After the court declined in October to review lower-court rulings that overturned bans on same-sex marriage in several states, 56 percent in a Post-ABC poll supported the decision, similar to overall gay-marriage support at the time.

The Supreme Court is reviewing a decision by another federal appeals court that upheld restrictions in Michigan, Ohio, Tennessee and Kentucky.

The latest Post-ABC poll was conducted by telephone April 16 to 20 among a random national sample of 1,016 adults, including users of land-line and cellular phones. The margin of sampling error for overall results is 3.5 percentage points.

Peyton M. Craighill contributed to this report.