His remarks could refer to Saudi Arabia, the United Arab Emirates or Bahrain - all close U.S. military allies that consider Iran a menace because of its support for militant groups in the Middle East.
The self-styled "Islamic State" has also claimed responsibility for the attack but like the other militant group, it did not provide any evidence.
Iran's President Hassan Rouhani vowed earlier Saturday to boost his country's ballistic missile capabilities despite Western concerns that were cited by his U.S. counterpart Donald Trump in May when he abandoned a landmark nuclear deal with Tehran. Rouhani was in Tehran giving a speech. "But they are linked to America and Mossad", Israel's intelligence agency.
This picture taken on September 22, 2018 in the southwestern Iranian city of Ahvaz shows an Iranian soldier carrying an ijured comrade at the scene of an attack.
Iran will be scrambling to determine the motives for the Saturday's high-profile attack as it faces growing US pressure. The statement said those sponsoring "terrorism in the region won't be able to achieve their plots using these sordid crimes".
One of the victims was a four-year-old girl.
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Teheran also summoned diplomats from Denmark, the Netherlands and Britain for allegedly hosting members of the group suspected of links to Saturday's attack.
The agency cited "knowledgeable sources" without elaborating.
The Islamic Revolutionary Guards Corp (IRGC) has been the sword and shield of Shia clerical rule in Iran since its 1979 Revolution. "Iran will respond swiftly and decisively in defense of Iranian lives", tweeted Iranian Foreign Minister Javad Zarif.
Zarif said that children and journalists were casualties in the attack.
He did not immediately elaborate. The province in the past has seen Arab separatists attack oil pipelines. The agency did not elaborate.
Ahvaz is in the centre of Khuzestan province, where there have been sporadic protests by the Arab minority in mainly Shi'ite Iran.
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IRNA reported that civilians, including women and children, who were watching the parade in the southwestern city Ahvaz, are among the dead and injured.
Saturday's attack in Ahvaz killed at least 25 people and wounded over 60.
Iranian local media reported that gunmen wearing military uniforms fired at the Iranian forces during a military parade, an attack that lasted for about 10 minutes.
June 7, 2017, gunmen and suicide bombers had attacked the Parliament and the mausoleum of imam Khomeini in Tehran, killing 17 people dead and dozens injured, the first attacks claimed by the group islamic State (EI) in Iran.
There was no immediate elaboration.
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