The group holding nine foreign oil workers in the Niger Delta say they have attacked another oil facility on Monday and blown up a military vessel.
The rebels threatened to step up their attacks
Three Americans and a Briton and Filipino were among those abducted on Saturday while laying a Shell pipeline.
Oil giant Shell has shut down its operations in the west of the delta and has cut production by 450,000 barrels a day, one-fifth of Nigeria's oil output.
The latest attacks have not been confirmed by the Nigerian authorities.
But the BBC's Alex Last says that what is worrying for the oil industry is that these militants have proved they can launch repeated coordinated attacks before retreating to their camps hidden amongst the forests and creeks of the Nigel Delta.
The unrest in Nigeria's main oil-producing area has led to an increase of more than $1 a barrel - to $61.15 - in early trade on Monday morning.
Leaders of the region's Ijaw community say they are heading into the creeks in search of the hostage-takers - known as The Movement for the Emancipation of the Niger Delta (Mend).
They say they support the youths' demand for using more oil wealth to improve the impoverished Delta region, but they oppose hostage-taking.
Mend say they will decide the hostages' fate in the coming days and have threatened more attacks, including firing rockets at tankers.
They said they attacked a Shell oil facility and a navy vessel on Monday.
"Both were destroyed with explosives," the group said in an e-mail.
Nigeria's government has assembled a team to negotiate their release and they are on their way to the region.
The BBC's Alex Last in Nigeria says hostages are usually released unharmed after some sort of deal, sometimes political but mostly financial.
He says Mend has a political agenda of securing greater control of the oil wealth and unlike most previous kidnappings, this group has proved it is serious by staging well-organised attacks that have drastically cut Nigerian oil exports.
The nine hostages were working for Willbros, a US engineering firm which is a Shell sub-contractor, in the Forcados river, 50km (30 miles) west of the oil port city of Warri, when they were abducted.
In an e-mail to the Associated Press news agency on Sunday, the hostage-takers said they had not yet decided what to do with their captives.
"They are being moved around with our units and may likely only be killed in a crossfire," AP quoted the group as saying.
"We have not reached a decision on what to do with these individuals... The next few days will determine what steps we will take," the statement read.
The rebels said they launched Saturday's attacks to avenge a series of helicopter strikes on local Ijaw villages.
The Nigerian military said it targeted barges being used by militants to smuggle stolen oil.
Nigeria is Africa's leading oil exporter and the fifth-biggest source of US oil imports. But despite its oil wealth, many Nigerians live in abject poverty.