Canada and the European Union have been trying to hammer out a free trade agreement for several years.
Alward said lower tariffs on Canadian seafood could mean more exports to Europe and that could increase demand, leading to higher prices for fishermen.
But Alward said his support for the CETA (Comprehensive Economic Trade Agreement) negotiations are not unconditional.
"Thus far, with what we've seen, we believe this is good for New Brunswick, but the work is not finished,” he said.
"Until the negotiations are finished and the recommendations are completed, I'm not prepared to support one way or the other."
Alward said he is particularly interested in making sure the province's supply management systems for agriculture are not affected.
Eggs, chicken and dairy products are subject to quotas meant to protect provincial producers from outside competition.
The Canada-EU negotiations were originally supposed to conclude in 2011, but that timeline was extended.
Canada is hoping the trade deal could boost trade by as much as 20 per cent with the EU and diversify its economy away from reliance on the United States.
A main push for the trade agreement from the EU’s perspective is to show the Americans they are willing to make reasonable compromises in future talks when it comes to agriculture.
New Brunswick’s Opposition Liberals tried to pin down Alward on the trade deal on Tuesday during question period.
Newfoundland and Labrador Premier Kathy Dunderdale revealed this week the Harper government tried to get her to trade away provincial fish processing rules to help secure the trade deal with the European Union.
Liberal Leader Brian Gallant said his party supports a trade deal if it can open up new markets for New Brunswick businesses.
But he said he wants to make sure Alward isn't trading away any other rights under pressure from the prime minister.
"We'd like to know what's happening behind the scenes, what our premier has been saying to the prime minister, what trade concessions, if any, he's been asked to make,” he said.
Alward said the prime minister has not asked for any similar demands similar to Newfoundland and Labrador.