According to NASA's Space Educator's Handbook:
As the men in Apollo 13 experienced what no men had undergone before, millions followed the developing drama by radio and television in public squares, private homes, schools, offices and factories. Pope Paul, at an audience in St. Peter's Basilica for 10,000 Romans and tourists, said "We cannot forget at this moment the lot of the astronauts of Apollo 13. We hope that at least their lives can be saved." Prolonged applause followed. Prayers were said at Jerusalem's Wailing Wall and on the floor of Chicago's Board of Trade.
On Tuesday, April 14, the U.S. Senate adopted a resolution which urged all businesses and communications media to pause at 9 p.m., their local time, to "permit persons to join in prayer for the safety of the astronauts."
Offers of assistance with ships to aid in the recovery came from many nations. The Associated Press quoted the Russian news agency Tass as saying that four Soviet ships were steaming toward the splashdown area, one of them the Chumikan, a missile tracker equipped with a helicopter. Tass said the Chumikan and fishing trawler No. 8452 were ordered to join the cargo carriers Academician Rykachev and Novopolotsk converging on the Pacific target area.
Premier Aleksei N. Kosygin sent a message saying: "I want to inform you (U.S. Government) the Soviet Government has given orders to all citizens and members of the armed forces to use all necessary means to render assistance in the rescue of the American (Apollo 13) astronauts."
And what about the radio transmissions? A contemporary newspaper article in the Pennsylvania Reading Eagle says:
The Soviet government ordered all Soviet radio transmitters using frequencies close to those of Apollo 13 to maintain silence from the spacecraft's entry into the earth's atmosphere to its splashdown in the Pacific today.
An official announcement said the precaution was being taken in response to the "request of the U.S.A. administration and bearing in mind the exceptional importance of safeguarding stable, continuous radio communications with the Apollo 13 spacecraft."
The government also said a whaling expedition of several Soviet ships in the Pacific had been alerted to aid in the recovery of the astronauts if needed. The Soviets announced earlier that four other ships were heading for the splashdown target area to render any assistance needed.