"Today we're sharing that we've recently seen significant cyber activity by a threat group we call Phosphorus, which we believe originates from Iran and is linked to the Iranian government," the BBC quoted Microsoft as saying in a statement on Friday.
Phosphorus, it said, made more than 2,700 attempts to identify people's email accounts over a 30-day period in August and September. It then attacked 241 accounts.
"The targeted accounts are associated with a US presidential campaign, current and former US government officials, journalists covering global politics and prominent Iran living outside Iran," the statement added.
Currently, 19 Democrats are seeking to be nominated as their party's candidate to stand against President Donald Trump in 2020, while three Republicans have said that they planned to challenge him.
Microsoft however, did not identify which specific campaign was targeted.
According to Microsoft, only four accounts were eventually compromised, and none of these were associated with a campaign, nor any former or current officials, the BBC reported.
The hackers tried to take over the accounts, in attacks Microsoft called "not technically sophisticated". The company has told account holders affected and helped to protect them.
There has been increasing global concerns about foreign-sponsored election interference via hacking.
In July, former US Special Counsel Robert Mueller concluded that Russia systematically interfered in the 2016 election with the intention of benefitting Trump - although he did not establish collusion in a crime.
The same month, Microsoft said it had told almost 10,000 customers they had been targeted or compromised by nation-state attacks.
( With inputs from IANS )