Hosts Germany are still not certain captain Michael Ballack will be fit for the opening World Cup game against Costa Rica on Friday.
England took heart, though, after their major injury worry, striker Wayne Rooney, trained with rest of the squad.
Ballack said he assumed he would recover from a calf injury for the first of the 64 games at the world's most-watched sporting event but Germany's coaching staff were more cautious.
"We hope that after a little rest and the work of the medical department he will be fit," assistant coach Joachim Loew said on Tuesday, three days before the Group A match in Munich.
"It's just a little calf muscle problem but it is a nagging injury," added Loew.
The midfielder, who joined English champions Chelsea last month, is the outstanding talent in a Germany side otherwise lacking in creativity. He was injured in a 3-0 win over Colombia last Friday, Germany's last warm-up match before the finals.
Ballack missed training on Monday but took part in an indoor workout on Tuesday morning.
"I think it will continue improving day by day and I assume I will be able to play on Friday," the player said.
ROONEY TRAINS
Rooney, who broke his foot on April 29, took part in the first 20 minutes of a session at England's training base near Baden Baden. He then did a mixture of running, sprinting and ball work on his own with the fitness coach.
Rooney will have a scan in Manchester on Wednesday which should determine whether he can play any part in the tournament.
"I think he looks very good," England coach Sven-Goran Eriksson said, though he also added a note of caution.
"It's totally up to the surgeons, the specialists, the doctors and physios. I can't judge it," he said.
Serbia & Montenegro tried to get the focus back on their preparations after the coach's son withdrew from the squad in the wake of angry complaints by fans that his selection had been due to nepotism.
Coach Ilija Petkovic said his son Dusan had returned home from their training camp in Felden, Austria to "put an end to an ordeal" while the rest of the players flew to Germany.
On arrival at Muenster airport in Germany, captain Savo Milosevic told Reuters the players were in good spirits and hoping to reach the second round from a difficult group that also features Argentina, Netherlands and Ivory Coast.
"The team spirit is outstanding and nothing can disrupt the atmosphere we have got," he said.
Germany has forged an unprecedented level of international police cooperation in an effort to prevent hooliganism overshadowing the month-long tournament.
Foreign police officers who specialise in tracking hooligans are being deployed across the country.
"Soccer fans from all over the world will feel not only safe but at home in our country," Interior Minister Wolfgang Schaeuble said.
