DUBAI, June 8 (Reuters) - Overnight exchanges of fire between Iran and Israel will only worsen an already "chaotic diplomatic process" with the United States, Iranian Foreign Ministry spokesperson Esmaeil Baghaei said on Monday, adding that Tehran was exchanging messages with Washington in an atmosphere of "extreme suspicion".

Baghaei said Israel's actions in Lebanon, whether carried out with U.S. knowledge and consent or not, were aimed at sabotaging diplomacy. He said Washington, as a party to the April 8 ceasefire, bore direct responsibility for any violations, including attacks attributed to Israel, and he added that the world should be concerned about a broader regional conflict.

"The United States bears direct responsibility for any action the Zionist regime (Israel) takes in relation to violating regional peace and security against Iran," Baghaei said.

He said the visit of Pakistan's interior minister to Tehran on Sunday was part of efforts to continue indirect exchanges with Washington.

Separately, Baghaei said Iran would respond to any resolution against it at this week's meeting of the U.N. nuclear watchdog's Board of Governors.

He accused International Atomic Energy Agency chief Rafael Grossi of disregarding the realities of the conflict and holding biased political views that harmed the agency's legitimacy.

(Reporting by Dubai Newsroom, Editing by Louise Heavens and Hugh Lawson)