Republican presidential candidate Donald Trump gives a thumbs up to supporters after speaking at a campaign rally on April 11, 2016 in Albany, New York. (credit: Eduardo Munoz Alvarez/Getty Images)

NEW YORK (CBSNewYork) — A new national poll out Thursday shows GOP front-runner Donald Trump still holds a double-digit lead over his nearest rival, Ted Cruz, but that his lead is smaller than it was last month.

The CBS News poll found that 42 percent of Republican primary voters would like to see Trump as the party’s nominee followed by Cruz at 29 percent and John Kasich at 18 percent.

MORE: Campaign 2016 Coverage | Full Poll Results From CBS News

Trump’s lead over Cruz is now at 13 points, down from 20 points last month, according to the poll.

The billionaire businessman’s margin against the Texas senator has also tightened among men, very conservative voters and those with incomes over $50,000, the poll found.

In a two-man race between Trump and Cruz, the poll shows that Trump would still lead 48 to 38 percent.

In the event of a contested convention, 63 percent of Trump supporters say he should run as an independent or third-party candidate if he earns more delegates than the other candidates but does not become the party’s nominee.

Among Republican primary voters overall, a third thinks in that case, he should run independently.

If none of the Republican candidates receive a majority of their party’s delegates by the GOP convention in July, 63 percent of Republican primary voters think it would be bad for the party, including 80 percent of Trump supporters and half of those supporting either Cruz or Kasich.

The poll was conducted by telephone April 8-12, 2016 among a random sample of 1,320 adults nationwide, including 1,098 registered voters and 399 registered voters likely to vote in a Republican primary.

The error due to sampling for results based on the entire sample could be plus or minus three percentage points. The margin of error for the sample of 399 Republican primary voters could be plus or minus six percentage points.