The report cited Middle Eastern and American officials.
A series of blasts in the past few weeks have hit weapon depots and bases belonging to paramilitary groups in Iraq, many of them backed by Israel's regional foe Iran.
The groups blamed the United States and Israel for the blasts on Wednesday.
The Times specifies a July 19 attack on a base near Baghdad that an unnamed "Middle East intelligence official" said was used by the Iranian Revolutionary Guards to move the weapons. The attack, which was reportedly launched from inside Iraq, destroyed "a cargo of guided missiles with a range of 125 miles."
The report said that an Iraqi military official confirmed a base was hit, killing three people – including one Iranian.
The NYT quoted a senior American official as saying that "Israel was pushing the limits" by striking targets in Iraq and that such action could result the U.S. Army having to leave its bases in the country.
The Iraqi government on Thursday avoided attributing the strikes to any country, with Iraqi national security adviser Falih al-Fayadh saying Baghdad did not wish to take sides in any conflict between Iran and other countries.
Meanwhile, Prime Minister Benjamin Netanyahu hinted Thursday of possible Israeli involvement in attacks against Iranian-linked targets in Iraq.
In an interview with Russian-language Israeli television Channel 9, broadcast on Thursday, Netanyahu was asked whether Israel would operate against Iranian targets in Iraq if needed, he said:
"We are operating - not just if needed, we are operating in many areas against a state that wants to annihilate us. Of course I gave the security forces a free hand and instructed them to do anything necessary to thwart Iran's plans."
Netanyahu did not directly name Iraq as one of those areas.
Israel says it has carried out hundreds of strikes in Syria, some of them against Iranian targets, to prevent Teheran from establishing a permanent military presence there and to stop advanced weapons reaching its proxies in the area.
Israeli officials suggested recently they viewed Iraq, whose main ally is Iran, as more of a threat than in recent years, but have not directly commented on the recent blasts at Popular Mobilization Forces (PMF) sites in Iraq.
On Wednesday, the PMF, the umbrella grouping of Iraq's mostly Shi'ite Muslim paramilitary groups, said the United States had allowed four Israeli drones to enter the region accompanying U.S. forces and carry out missions on Iraqi territory.
The Pentagon denied involvement.
The U.S.-led coalition, in Iraq to fight remnants of the Islamic State group, dismissed the statement.
As tensions between Washington and Tehran increase, Iraq finds itself caught between neighboring Iran, whose regional influence has grown in recent years, and the United States.
Iraqi Prime Minister Adel Abdul Mahdi last week ordered all ammunition dumps belonging to the armed forces or paramilitary groups to be moved outside of cities.