Abadi had told reporters Wednesday that there was "no logic to the operation at all in the first place," according to The New York Times. "Mainly the problem of Yemen is within Yemen."
But the Iraqi leader told a Washington think tank on Thursday that while he was "frank" about the situation in Yemen, "my intention is not to criticize anybody."
Abadi, a Shiite, told the Center for Strategic and International Studies: "We are on the same boat in the region. If anybody makes a hole in that boat, we all will sink.
"We have suffered so much from wars in Iraq. We are very sensitive to wars, very sensitive to humanitarian costs.
"And in our own belief we think an end to this war of Yemen must be very soon and the only way forward is a political solution by Yemenis themselves."
Signup to our newsletter and follow us on Facebook and Twitter!
He stressed: "We are only giving some advice, some opinion on this. We don't intervene in their own affairs, and ask them not to intervene in our own."
Diplomatic relations between Saudi Arabia and Iraq were severed in 1990, but restored in 2004 after the fall of Saddam Hussein's regime.
Saudi Arabia announced in January it was sending a delegation to Iraq ahead of opening an embassy in Baghdad, where its last mission closed nearly 25 years ago.
Abadi said he had learned Wednesday that Riyadh has now nominated a new ambassador and said the Saudi compound was "ready and renovated," adding that having a Saudi embassy in Baghdad "makes our job much easier."
The Saudi-led drive to push out the Huthi militias and restore to power ousted President Abedrabbo Mansour Hadi is now in its fourth week.
US pointman on Iraq, ambassador Brett McGurk, said the reopening of the Saudi embassy in Baghdad would be a "significant milestone."
"We think it's very important that the prime minister has re-established ties with all of the regional leaders and they don't have to agree on everything, but there are a lot of common interests," McGurk told the Washington-based Arabic language Radio Sawa.