The long, bitter struggle between the rulers of Iraq Communist Party has broken into the open again.

Iraq's Arab Baath Socialist Party government has announced another purge of alleged Communists in the armed forces. Las night the Communist Party's daily newspaper was suppressed for a month, Earlier, the Communists stopped participating in the nominal front of political parties tolerated by the Baathists as a show of national unity.

The suspected Communists in the Army, accused of plotting a coup d'etat, are expected to be executed. Diplomatic analysts are speculating that the Communists, with their ranks now depleted by arrests and executions, may finally abandon the pretense of cooperating with the Baathists and go underground.

In the past, repeated bloody purges of Iraq's Communists have put severe strains on this country's relations with the Soviet Union, Iraq's arm supplier. Informed diplomatic sources and Iraqi officials say the ruling Baathists, of whom ideological and political independence are an article of faith, remain suspicious of Soviet intentions but they are apparently trying to avoid any open show of disagreement with Moscow.

The announccement by the Iraq news agency that the Communist paper had been closed for unspecified violations of the press law was accompanied by a report the Saddam Hussein, vice chairman of the Revolutionary Command Council that runs the county had sent a message to the Soviet leadership praising Soviet-Iraqi cooperation. The occasion was the seventh anniversary of the signing to the Soviet-Iraqi treaty of friendship and cooperation.

Saddam Hussein was in Moscow in December for a visit that appeared to restore warmth to ties chilled by Iraq's execution las summer of 21 soldiers accused of conducting Communist political organization in the ranks. Since then, however, another 27 military men have been taken into custody on the same charge, indicating renewed Iraqi suspicion of the Communists.

Earlier this week, Saddam Hussein confirmed the purge to Arab journalists meeting in Beirut and said that while his coutnry wants to maintain friendly ties to Moscow, "We reject the wide expansion by the Soviet Union in the Arab homeland."

In an interview yesterday, Tarek Aziz, a leading member of both the government and the Baath party hierarchy, said that "after the executions of last summer, we found more Communist cells in the armed forces this year. We have new prisoners. They will be judged by the law and face thrir fate." They were arrested, he said, not because they were Communists as such, but because "political activity in the armed forces means they were planning a coup."

He said Iraq "has achieved an independent revolution and we are keen on political, cultural, economic and ideological independence. We cannot sustain a party inside our country which has unnatural ties with foreign blocs." He said those executed last summer were "spies" and that any Iraqis suspected of working for foreign interests, Communists or otherwise, would be dealt with the same way.

The Iraqi Communist Party, one of the strongest in the Arab world, has been a power in Iraqi politics for 30 years, despite repeated purges by the Baathists and their predecessors.

The party's roots are among the minority Kurds of northern Iraq. The Kurds' separatist demands flared into armed rebellion in the early 1970s and the "Kurdish question" remains once of the most troublesome for any Iraqi government, so the Communists with links to Kurdistan are doubly suspect. Diplomatic sources here said they believed the latest roundup of alleged Communists in the Army was linked to political activity among the Kurds, but no details of the charges have been made public.