-LRB- CNN -RRB- -- New Hampshire 's Senate has approved a bill allowing same-sex couples to marry , but critics and supporters of the legislation say their work is n't over . New Hampshire could become the fifth state to allow same-sex marriage if a bill becomes law . `` We were obviously disappointed , '' Kevin Smith , executive director of the conservative Cornerstone Policy Research Action group , said Thursday . `` We do n't think the voters are going to forget about it . '' On the other side , members of the New Hampshire Freedom to Marry Coalition , a group that has worked since 2001 for same-sex marriage , were `` absolutely thrilled , '' said Mo Baxley , its executive director . But noting that the bill is returning to the House of Representatives for consideration of changes made by the Senate , Baxley added , `` I think the work continues . '' Her organization will encourage supporters to contact their representatives ahead of the House vote , she said . On Wednesday , the Senate voted 13-11 in favor of the bill , which differs from the House-approved version in that it distinguishes between civil and religious marriage . It allows each religion to decide whether to acknowledge same-sex marriage but extends the option of civil marriage to any two individuals , said state Senate spokeswoman Anne Saunders . The House , which passed the earlier version last month by a margin of seven votes , 186-179 , must approve the changed version before it can be sent to Gov. John Lynch , a Democrat who has questioned the need for the bill . After the Senate vote , Lynch released a statement saying he believes that `` the fundamental issue is about providing the same rights and protections to same-sex couples as are available to heterosexual couples . This was accomplished through the passage of the civil unions law two years ago . '' Lynch signed the state 's civil unions law in May 2007 . `` To achieve further real progress , '' he added , `` the federal government would need to take action to recognize New Hampshire civil unions . '' Earlier this month , the governor said he believes the word `` marriage '' should be used only to describe a marriage between a man and a woman , the New Hampshire Union Leader in Manchester reported . `` I think the word ` marriage ' is reserved for a marriage between a man and a woman , and I think the real issues really are rights and protections for gay and lesbian couples , '' he told reporters on April 15 , according to the newspaper . Smith said his organization , which was established in 2000 , would `` lobby hard '' to get the governor to veto the bill . He said he expected it to pass the House . `` Look , this is a matter of holding the governor accountable , '' he said . `` He 's been very public with his views on same-sex marriage in the state . ... We 'll see if he was misleading the voters of New Hampshire or if he 'll stand by his word and actually veto it . '' Were the bill to become law , New Hampshire would become the fifth state allowing same-sex marriage , joining Connecticut , Vermont , Massachusetts and Iowa . Only Vermont has established the practice legislatively . CNN 's Taylor Gandossy contributed to this report .