On the morning that Hamas raided Israel last year, a top Israeli general called his prime minister, Benjamin Netanyahu, to tell him that hundreds of militants appeared to be preparing to invade.

Now, aides to the prime minister are under investigation for altering details about that call in the official record of Mr. Netanyahu’s activities that day, according to four officials briefed on the investigation.

The investigation is seen as deeply sensitive in Israel, where the question of what Mr. Netanyahu knew in advance of Hamas’s invasion, and when he was told, could prove crucial to his political future. It is expected to play a key part in a postwar assessment of the role political and military leaders may have played in one of the worst military failures in Israel’s history.

The accusation is just one of several leveled at Mr. Netanyahu’s aides in recent weeks. While Mr. Netanyahu himself is not a subject of a police inquiry, officials in his office are under investigation for trying to bolster his reputation throughout Israel’s war with Hamas by leaking classified military documents, altering official transcripts of his conversations and intimidating people who controlled access to those records.

Though disparate and complex, the cases have helped foster the impression among Mr. Netanyahu’s critics that his team has used illicit means to improve how he is perceived, at the expense of either the truth or national security, or both. Mr. Netanyahu and his office have denied the accusations, countering that it is his accusers who, by spreading falsehoods, have undermined Israel at a time of national peril.

The full extent of the new claims has not been revealed because most of them are subject to a gag order. Officials who told The New York Times about the investigations did so on the condition of anonymity because they were barred from speaking publicly about the matter.