Iran's daily novel coronavirus caseload surpassed 5,000 infections -- a new record -- according to official figures announced Tuesday, as death rates remain high.

Health ministry spokeswoman Sima Sadat Lari said the country had registered a record 5,039 new infections in the previous 24 hours, bringing the total number to 539,670.

There were also 322 new deaths, as the worst-hit country in the Middle East counted 31,034 fatalities since February.

Government spokesman Ali Rabii told a press conference that "the spread of the virus is rising in 12 provinces including Tehran, and nine provinces are on alert", urging "cooperation" to curb its transmission.

Iran announced a record 377 deaths on Monday, and has made several grim announcements of record-high virus cases and fatalities in recent weeks.

President Hassan Rouhani said Monday that the country was now "facing a larger wave of this virus" and called on the health ministry to increase daily testing.