SAO PAULO (Reuters) - Stevedores at Brazil's Santos and Rio de Janeiro ports entered the second day of a strike to protest proposed legislation that may open terminals to new private-sector investments.

The strike began unexpectedly at midday on Tuesday at Brazil's main southeastern ports of Santos, Paranagua and Rio de Janeiro. The National Stevedores Union said on Wednesday, however, that the strike at Paranagua had ended.

"The strike at Santos will continue, and we expect it to spread to other ports in the northeast of Brazil," Santos Stevedores Union President Rodnei da Silva said.

He added that the dock workers were concerned that the reform bill in Congress did not sufficiently protect stevedores' rights because it would allow potential new terminal investors to contract nonunion labor.

The lower house of Congress failed to reach a vote on the bill after 16 hours of debate on Tuesday. The session was suspended more than once as lawmakers argued over the legislation, which may bring billions of dollars in new investments and lower the "Brazil cost" of doing business in the country.

Brazilian port terminals charge some of the world's highest prices to move goods. Some of the high cost stems from labor agreements, but red tape, taxes and lack of competition between terminals are also to blame.

The bill will come up for debate again in the lower house on Wednesday. If approved, it will then go to the Senate for a vote.

President Dilma Rousseff has made the bill a high priority for her push to improve Brazil's underdeveloped infrastructure, which has become a drag on economic growth.

The strike has affected the movement of ships through Santos, with 14 of the 35 vessels at the berths not loading due to the strike, according port spokesman Alexandre Soares.

Shipping agent Williams said the strike did not affect the loading of bulk raw sugar at the port, but has slowed the loading of bagged sugar because of the need for stevedores.

Typically bulk cargoes such as soy and corn are less affected by labor strikes because they require few workers. The movement of container goods such as coffee, bagged sugar and meats are more vulnerable to strikes.

Officials at Paranagua port said movement there was returning to normal after the strike slowed operations on Tuesday.

Brazil is in the middle of exporting a record soy harvest, while coffee and sugar crops are due to hit its overburdened ports within weeks. Even a one-day stoppage would lengthen already-long queues for ships and rack up tens of thousands of dollars in costs for idle ships.

(Reporting by Reese Ewing and Caroline Stauffer; Editing by Peter Murphy and Lisa Von Ahn)