The unions said Nigeria's federal, state and local governments should open a dialogue with the militants to resolve the crisis that has shut in 455,000 barrels a day of crude oil.
Leaders of Petroleum and Natural Gas Senior Staff Association of Nigeria, or Pengassan, and the National Union of Petroleum and Natural Gas workers, or Nupeng, said a strike would only escalate the crisis in the Niger Delta region.
"We cannot shut down flow stations now - that's why we call for dialogue between the government and the communities involved," Elijah Okugbo, general secretary of Nupeng told reporters.
Okugbo said the crisis in the Niger Delta was "politically motivated" and there was nothing the unions could do other than call for calm as a strike now could endanger the nine expatriate oil workers being held by the militants.
"We don't want to play into the hands of the hostage-takers," Okugbo said. "If we declare an ultimatum now, they will hold onto the hostages," he added.
However, he warned that the unions would meet again if there wasn't a quick resolution.
Militants attacked oil facilities Saturday in the Niger Delta, kidnapping nine employees of Wilbros Engineering, a contractor to Shell Petroleum Development Company of Nigeria - a unit of Royal Dutch Shell (RDSB.LN).
Peter Esele, acting president of Pengassan, said the government's slow response to issues in the oil industry, had contributed to the escalation of the crisis in the Niger Delta.
"In 2003, we requested bullet-proof speedboats, but it was only three days ago that the boats arrived," he asked.
The government of the Niger Delta Monday set up a committee, headed by an Ijaw leader, to negotiate with the militants and secure the release of the hostages.
This story was supplied by MarketWatch.
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