NatWest was forced to issue an announcement yesterday after its share price leapt 16p to 651p on Wednesday.
The shares eased 1p to 650p yesterday, following a week in which they have risen 10 per cent.
The British bank has accepted that Bancorp, although making healthy profits, is too small to take part in the "merger mania" of the US banking sector, where retail banks are paying top dollar to expand across state lines.
Richard Goelz, NatWest's finance director, said: "Given the way that the consolidation [in banking] is accelerating not just nationally but in Bancorp's own market of metropolitan New York, it became evident that we would have to make a major acquisition in the face of ever stronger competition - or divest.
"Bank share prices are very strong right now. We felt we could extract maximum value by divesting now," Mr Goelz said.
Analysts are expecting Bancorp, the third-biggest bank in New Jersey, to go for at least $4bn, or twice book value.
Recent American deals have seen banks going for 1.4 to 2.8 times book value.
Mr Goelz said NatWest's "strong preference" was for payment in cash rather than shares, and since most recent US deals had been paid for in paper the Bancorp price would reflect that.
The finance director, an American, stressed that the decision to sell was not connected with any possible other deal NatWest may or may not do.
The City is certainly watching keenly what NatWest will do with the proceeds. Analysts are virtually unanimous that it will get the thumbs up if NatWest buys back shares, as Barclays recently did, and that an adventurous acquisition of, say, a Wall Street investment bank would be poorly received.
Candidates to buy Bancorp include HSBC Holdings, ABN Amro and US banks, Nations Bank and Bank of America. In turn, analysts speculate that NatWest may then try to buy Mercury Asset Management, recently demerged from Warburg, or more likely a "middle-ranking" fund management business such as Henderson Crosthwaite or Gartmore Investments.
The move came on a day of frenzied stock market action involving five separate banks.
Royal Bank of Scotland's shares rose 3p to 456p on speculation that it may also take advantage of the buoyant market in US banks and sell its American Citizens Financial operation.
Also involved in the sell-off frame, Standard Chartered finished 12p stronger at 479p amid rumours that the bank is selling its securities trading operation to the Bank of China. Standard denied the rumours.
Bank of Scotland saw its shares unchanged at 246p as Standard & Poors warned it may downgrade its share rating, following the Scottish acquistion of WestBank of Australia on Wednesday for pounds 442m.
Bancorp under NatWest
1979 NatWest buys first retail subsidiary in New York metropolitan area
1989-91 Bancorp makes total losses of $1bn on property loans John Tugwell sent to US to turn it around
1992 Bancorp returns to profit
1993-4 Bancorp makes two acquisitions in New Jersey area
1995 NatWest decides to sell Analysts expect price tag of $4bn plusReuse content