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Three weeks until the first presidential nominating contest, Donald Trump and Ted Cruz are running neck and neck in Iowa, while Hillary Clinton and Bernie Sanders are also locked in a tight race in the Hawkeye State.

What’s more, Clinton and Sanders are within the margin of error in New Hampshire, while Trump has built a 16-point lead in the same state.

Those are the results of two brand-new NBC News/Wall Street Journal/Marist polls – the first NBC/WSJ/Marist early-state surveys of 2016, which for the first time measure likely voters.

In Iowa, which holds its caucuses on Feb. 1, Ted Cruz leads Donald Trump by four points among likely caucus-goers, 28 percent to 24 percent – within the poll’s margin of error of plus-minus 4.6 percentage points. They’re followed by Marco Rubio at 13 percent and Ben Carson at 11 percent. No other Republican candidate gets more than 5 percent of the vote.

Yet among the larger universe of potential Iowa caucus-goers, Trump actually leads Cruz by two points, 26 percent to 24 percent, suggesting that a larger turnout could benefit Trump in the state. (Back in October’s NBC/WSJ/Marist poll, Trump was at 24 percent among potential caucus-goers, Carson at 19 percent, and Cruz and Rubio at just 6 percent.)

On the Democratic side, frontrunner Hillary Clinton holds just a three-point lead among likely voters over Bernie Sanders, 48 percent to 45 percent, while Martin O’Malley gets 5 percent.

But among potential Democratic caucus-goers, Clinton’s advantage grows to six points, 49 percent to 43 percent. (In October, Clinton’s lead here was 11 points, 47 percent to 36 percent.)

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New Hampshire: Four Establishment GOP candidates split up almost 45 percent of vote

In New Hampshire, which holds its presidential primaries on Feb. 9, Trump gets support from 30 percent of likely Republican primary voters.

He’s followed by Marco Rubio at 14 percent, Chris Christie at 12 percent, Ted Cruz at 10 percent, and John Kasich and Jeb Bush tied at 9 percent each.

That means that the four Republicans vying in the establishment lane of the GOP contest – Rubio, Christie, Kasich and Bush – are dividing up 44 percent of the total vote, according to the NBC/WSJ/Marist poll.

The GOP numbers are essentially unchanged among the larger pool of potential Republican voters in New Hampshire.

In the Democratic race, Sanders is ahead of Clinton by four points among likely primary voters, 50 percent to 46 percent, which is within the margin of error of plus-minus 4.8 percentage points. O’Malley is at 1 percent.

Among the larger universe of potential Democratic primary voters, Sanders’ lead increases to six points, 50 percent to 44 percent. In October, the Vermont senator held a nine-point lead over Clinton.

Sanders outperforms Clinton in general-election matchups

The NBC/WSJ/Marist polls also show that Sanders outperforms Clinton in hypothetical general-election matchups in these two presidential battleground states – something other surveys have found, too.

In Iowa:

Clinton leads Trump by eight points among registered voters (48 percent to 40 percent), but Sanders is ahead of him by 13 (51 percent to 38 percent);

Cruz tops Clinton by four points (47 percent to 43 percent), but Sanders beats him by five (47 percent to 42 percent);

And up Rubio is up by five points over Clinton (47 percent to 42 percent), while he’s tied with Sanders (44 percent to 44 percent).

In New Hampshire:

Clinton is ahead of Trump by just one point (45 percent to 44 percent), but Sanders tops him by 19 points (56 percent to 37 percent);

Cruz beats Clinton by four points (48 percent to 44 percent), but Sanders leads him by another 19 points (55 percent to 36 percent);

And Rubio bests Clinton by 12 points (52 percent to 40 percent), while Sanders leads him by nine points (50 percent to 41 percent).

The primary reason why Sanders tests better in these general-election matchups is due to his stronger performance with independent voters.

The NBC/WSJ/Marist polls were conducted Jan. 2-7. In Iowa, the poll measured 2,821 registered voters (+/- 1.8), 1,094 potential GOP caucus-goers (+/- 3.0%), 456 likely GOP caucus-goers (+/- 4.6%), 977 potential Democratic caucus-goers (+/- 3.1%) and 422 likely Dem caucus-goers (+/- 4.8%)

In New Hampshire, the poll measured 1,888 registered voters (+/- 2.3%), 887 potential GOP primary voters (+/- 3.3%), 569 likely GOP primary voters (+/- 4.1%), 690 potential Dem primary voters (+/- 3.7%) and 425 likely Dem primary voters (+/- 4.8%).