The man, aged 62 according to media reports, was taken on the remote South Alligator River late on Saturday afternoon.
His wife, son and daughter-in-law were said to have witnessed the attack, and the women had to drive two hours to the nearest lodge to raise the alarm while the son stayed behind to search for his father.
Superintendent Bob Harrison said there was always reason to hope, but "a crocodile attack is very serious and there are grave concerns".
"We received a call from the manager of the Gagudju lodge there that some people had walked in and told them (the man) had been taken by a crocodile," Harrison told ABC radio.
"I believe the son was involved in the initial search for his father, which is obviously traumatising and anyone's heart would go out to the family in that sort of incident."
Harrison said the search would be ramped up Sunday after overnight efforts failed to turn up any sign of the man or crocodile.
The creatures are a common feature of Australia's tropical north, and their numbers have increased steadily since the introduction of protection laws in 1971, with government estimates putting the population at 75,000-100,000.
Saltwater crocodiles can grow up to seven metres (23 feet) long and weigh more than a tonne.
Saturday's attack is Australia's first fatality since January, when a 12-year-old boy was taken by a crocodile in the Kakadu national park, a sprawling World Heritage-listed nature and cultural reserve in Australia's Top End.
Another boy suffered bite wounds in that incident as he fought the crocodile off.
According to the international CrocBITE database of attacks set up at Australia's Charles Darwin University last year, there have been 66 fatalities globally so far in 2014.
The database was set up with the aim of firming up anecdotal reports that harmful or fatal incidents are increasing. There were 76 fatalities recorded by CrocBITE over the same period in 2013.