Updated at 11:20 a.m.: to note the increase in Texans who cite gun violence as the most important issue facing the state, though far more cite immigration; and add the margin of error for the Democratic sample.

AUSTIN — A new poll has former vice president Joe Biden leading Beto O'Rourke in the Texas Democratic presidential primary, while President Donald Trump's job-approval rating edged up slightly from a year ago.

The Texas Lyceum poll, released Thursday morning, brought mixed tidings for state GOP leaders. While Gov. Greg Abbott and Lt. Gov. Dan Patrick enjoy high personal job ratings, Texans' views of the state economy's strength continue to sag.

The poll, completed before last weekend's mass shooting in Odessa and Midland, found what researchers called "a notable increase" in the percentage of Texans who said gun violence or gun control is the most important issue facing the state and the country. Immigration, though, remains the top issue on Texans' minds.

In a first for public polls, Massachusetts Sen. Elizabeth Warren moved into third place in the Texas Democratic contest for president, ahead of Vermont Sen. Bernie Sanders. Her 2-point lead over Sanders, though, was well within the new poll's margin of error — plus or minus more than 5 percentage points for the Democratic voters surveyed.

The poll showed Biden with 24% of likely Democratic voters in the Lone Star State, O'Rourke with 18%, Warren with 15% and Sanders with 13%.

California Sen. Kamala Harris and former federal Housing and Urban Development Secretary Julián Castro tied for 5th place, with 4% each.

O'Rourke, Castro need 'strong showing somewhere'

"This result is probably disappointing to Castro supporters, particularly his current standing among Hispanics in the state," University of Texas government professor Daron Shaw said in a written statement.

The Super Tuesday contest on March 3, when Texas and 13 other states hold primaries, is still six months away, noted Shaw, who is both an alumnus of Texas Lyceum's leadership training program and former research director for the group's poll.

Much could happen to alter the Democratic hopefuls' fortunes, Shaw said. After next week's debate in Houston, there are three more debates and four contests in early states in February.

"What is clear, though, is that both Castro and O'Rourke need a strong showing somewhere prior to March 3, 2020, in order to convince Texans that they stand a real chance," he said.

While Trump's approval rating edged up slightly, most Texans believe the country is on the wrong track and their view of the state economy dipped for the third consecutive year, the Texas Lyceum poll found.

Forty-eight percent of Texans believe Trump is doing a good job, while 51% feel he's doing a poor job. Last year, the Lyceum poll found 44% of all Texans approved of his job performance. Broken down by party, 79% of Texas Republicans gave Trump positive marks, while 80% of Democrats say he's doing a somewhat or very poor job.

Last month's Lyceum poll did not include head-to-head comparisons between Trump, the likely Republican nominee, and the Democratic candidates.

Dwindling lead for Biden in Texas?

Though its methodology and that of other public polls in Texas vary, the Lyceum poll supported national polls that have shown Biden's lead narrowing and Warren surging past Sanders.

In Texas, home to O'Rourke, the Quinnipiac University Poll in June showed Biden ahead of the former congressman and U.S. Senate candidate, 30% to 16%. Sanders was at 15%; and Warren, at 11%.

Last month, a poll by The Dallas Morning News and Emerson College had Biden at 27.7%, O'Rourke at 19%, Sanders at 15.7% and Warren at 13.7%. In that poll, South Bend, Ind., Mayor Pete Buttigieg was 5th with 7.2%.

Buttigieg fared more poorly in the Texas Lyceum poll: He and Minnesota Sen. Amy Klobuchar were in a tie for 7th place, with 3% each. Only three other Democratic candidates had more than 1%: New Jersey Sen. Cory Booker, entrepreneur Andrew Yang and Montana Gov. Steve Bullock, each with 2%.

Abbott, Patrick and views of economy

Abbott and Patrick are drawing better approval ratings from Texans than Trump — especially Abbott. But a majority of Texans believe the country is on the wrong track, and their views of the state economy dipped for a third consecutive year, the Texas Lyceum poll found.

Abbott wins positive reviews from 67% of Texas adults, with only 33% disapproving of the job he's doing as governor. While the Republican governor has 72% job approval among whites, he does well in Democratic-leaning racial and ethnic groups. Sixty-five percent of Hispanics express approval, and 57% of African Americans, the poll found.

Sixty percent of Texas adults approve of Patrick, with 35% disapproving and 5% unable to express an opinion.

Fifty-eight percent of Texans believe the country is on the wrong track, compared with 41% who say it's moving in the right direction.

Thirty-eight percent of Texans say the national economy is better off compared with one year ago, with equal shares (31%) saying it is worse off or about the same.

While 45% of Texans say the state's economy is better than the rest of the country's, 40% say it's the same and 15% say that Texas' economy is worse off. Last year, however, 63% said that Texas' economy is better off than the nation's.

The Texas Lyceum poll of 1,200 Texas adults was conducted Aug. 16 to Aug. 25. Of the respondents, 1,000 were reached on landlines and cellphones, while an additional 200 people in "hard to reach populations" were surveyed online. Poll-takers confirmed the 200 aren't registered to vote. The margin of error was plus or minus 2.83 percentage points.

For the sample of 358 likely Democratic voters, the margin of error was plus or minus 5.18 percentage points.