The Nigerian Maritime Administration and Safety Agency (NIMASA) said it had “commenced search (and) rescue operations” for the abducted crew from the MV Glarus.
The ship was attacked 45 nautical miles southwest of Bonny Island, near the southern city of Port Harcourt, as it travelled from Nigeria's commercial capital, Lagos, on Saturday.
NIMASA director-general Dakuku Peterside said the agency was working “to ensure that they are found and released unconditionally”.
The search and rescue was being conducted with the Nigerian Navy and other security agencies, he told a news conference in Lagos.
“The issue of piracy in the Gulf of Guinea is a challenge we acknowledge and we are determined to tackle it head-on,” he said, vowing “zero-tolerance” of the problem.
Kidnapping for ransom is rife across Nigeria, particularly in the oil-rich south where prominent individuals, members of their family and expatriates have regularly been seized.
Offshore, the Gulf of Guinea has become the world's piracy hotspot.
The International Maritime Bureau said in late July that there were six kidnappings of crews around the world in the first half of 2018. All of them were in the Gulf of Guinea.
Out of the 16 incidents in which ships came under gunfire in 2017, seven were in the waters which stretch 5,700 kilometres (3,541 miles) from Senegal to Angola.
During the first half of 2018, the crews of six ships were kidnapped by pirates, who are usually well-armed. Sometimes ships are held long enough for the cargo to be looted.
The MV Glarus' owners, Massoel Shipping, has said the pirates used long ladders and cut razor wire to get onto the vessel and take over the bridge. Twelve of the 19-strong crew were seized.
The Geneva-based company said it would not divulge the identities or the nationalities of the hostages for safety reasons but added it was in touch with their families.
But the Slovenian foreign ministry said on Monday that one of its nationals was among those taken.