The United States hopes Iraqis approve the draft constitution on Saturday, Vice President Dick Cheney (search) told FOX News on Friday, although Bush administration officials say they are not trying to influence the election.

"I think we're going to get a good vote and a big turnout and we certainly hope and expect the constitution will be approved," Cheney said in an exclusive interview with FOX News' Brit Hume. "It's very significant event. When you think about the course of the time here in Iraq, it's vital we get constitution in place and follow that with national elections in December."

Watch the Cheney interview on FOX News' "Special Report with Brit Hume" tonight at 6 p.m. EDT.

The vice president also echoed assurances President Bush received Thursday from U.S. soldiers in Iraq that the Iraqis' military capabilities are improving. Both Iraqi and U.S. forces clamped down with intensive security measures to prevent insurgent attacks on voters at the poll on Saturday.

However, State Department Deputy Spokesman Adam Ereli would not go so far as to voice support for the constitution.

Asked whether it matters to the United States if the constitution is accepted or rejected, Ereli said: "That's a decision for the Iraqi people."

Cheney said more than 200,000 Iraqi troops have been trained and equipped and are taking on more and more professional capabilities, though Pentagon officials said two weeks ago that fewer than 1,000 of them are able to replace U.S. troops.

As the interview was conducted, Bush's deputy chief of staff and chief political advisor, Karl Rove (search), testified for the fourth — and final — time before a grand jury investigating who leaked the name of a CIA operative to reporters. Reporters have named Rove as a source, as well as Cheney's chief of staff, Lewis "Scooter" Libby (search). But both men have said they may have learned of the operative, Valerie Plame (search), from other reporters, and have denied their comments about her were vindictive.

But the issue is so sensitive that Cheney wouldn't talk about anything related to it. Bush himself has refused to comment much on the topic, saying it's his policy to not comment on any ongoing investigation.

"Brit, I'm simply not at liberty to discuss the issue," Cheney said in the FOX News interview.

Cheney defended the nomination of White House attorney Harriet Miers (search) to replace Sandra Day O'Connor (search) on the Supreme Court.

Noting that Miers has helped the president with more than 200 other judicial appointments, Cheney added that the nominee's background was thoroughly researched. Plus, he said, the five years she's worked in the White House has given the president's most senior advisors a full understanding of her judicial philosophy.

"What I know about her views is having worked alongside her for five years. I also know this is a woman who graduated from law school back in the late 60s, when it was difficult to break into the profession," Cheney said.

Some conservatives have complained that Miers is not conservative enough and does not have enough of a judicial paper trial to be adequately judged on. Conversely, many Democrats have argued that Miers deserves a chance to be heard and seem to be muting many of their own arguments against the nominee so far.

An aide to the Senate Judiciary Committee on Friday gave a letter to FOX News from three of Texas' State Supreme Court justices voicing their "strongest support" for the Miers' nomination. The letter, addressed to panel Chairman Arlen Specter, R-Pa., and Ranking Democrat Patrick Leahy of Vermont, said one of Miers's most "significant contributions" to the state of Texas was her "effort to improve legal representation for the poor and under-served."

"Her 30 years of broad, real-world legal experience would be an asset to the Supreme Court," the justices wrote.

They added: "Together we represent 34 years of experience on the Texas Supreme Court. We feel confident that we know what it takes to be a justice — Harriet Miers exceeds that mark. We are united in affirming that Harriet Miers is an outstanding candidate and in offering our strongest support for her nomination to our nation's highest court.

FOX News' Wendell Goler contributed to this report.