( CNN ) -- Persuading Congress to ban assault weapons will be tough , New York Mayor Michael Bloomberg said Thursday . But it 's a fight the outspoken advocate of stricter gun laws says he 's determined to win . `` Getting rid of assault weapons , that is a tougher sell , and that 's what we 've really got to work on , '' Bloomberg said in an interview with CNN 's AC360Â° . `` I 'm optimistic , but it 's tougher . '' Bloomberg said he 's encouraging the roughly 800 mayors who are members of his Mayors Against Illegal Guns organization to start lobbying lawmakers and `` explain to them why constituents really want this done . '' Speaking a day after President Barack Obama announced a list of proposals to reduce gun violence , Bloomberg said the package -- which calls on Congress to reinstate the assault weapons ban , restrict ammunition magazines and expand background checks for gun buyers -- is `` reasonably comprehensive . '' And even though parts of the proposal will face an uphill battle , he said , that does n't mean it is n't a worthwhile fight . Obama-backed gun bills considered a longshot in Congress . `` There are lives involved here . And if you can save one life , is n't that worth trying ? '' Bloomberg said . `` And I always thought that you should address issues when they 're on the public 's conscience , while they 're being covered by the press , and you should try to do a complete job so you do n't have to go back again and again and again . '' Poll : Gun control support wanes . Republicans immediately rejected the Obama proposals as an attack on the constitutional right to bear arms . `` Nothing the president is proposing would have stopped the massacre at Sandy Hook , '' Sen. Marco Rubio , R-Florida , said in a statement . `` That 's probably true , '' Bloomberg acknowledged on Thursday . `` But that does n't mean that having fewer guns around is n't a better idea . '' Under New York 's stricter gun laws , he said , the city has seen murder and suicide rates that are lower than the national average . Last week , former House Speaker Newt Gingrich told AC360Â° that the evidence in Chicago tells a different story . A look at U.S. gun laws . `` Chicago has very strict gun laws . It is also the deadliest city in America , '' Gingrich said . Asked Thursday about Gingrich 's observation , Bloomberg said gun laws are n't a panacea . `` There 's no one solution to this , '' he said . `` This is , however , a very important step . Fewer guns means fewer murders . Fewer guns means fewer suicides . Fewer guns means you and your children are safer . '' Since last month 's shooting massacre at a school in Newtown , Connecticut , Bloomberg and his group have been at the forefront of a push for stricter gun laws . Opinion : A father 's murder , a plea on gun control . He 's said that more than 1 million people have signed a petition backed by the organization to tighten gun control laws in the wake of the Newtown shooting rampage . The group has spent millions on television spots calling for gun control , including an ad that ran nationally this week , featuring family members of victims killed by gun violence repeating the word , `` enough . '' On Thursday , Bloomberg sharply criticized the National Rifle Association for its approach to the gun control debate . After blaming video games for the Newtown shooting rampage , the organization released its own gun-related mobile video game . And on Tuesday night , the NRA released an ad accusing Obama of hypocrisy for being `` skeptical '' about placing armed guards at schools , when his two daughters are protected by the U.S. Secret Service . That was `` bad P.R . '' and an `` outrage , '' Bloomberg said . `` I think it 's just a bad strategy , '' he said , `` and they 're going to lose this battle . '' CNN 's Mark Preston , Dana Bash , Jessica Yellin and Tom Cohen contributed to this report . Watch Anderson Cooper 360° weeknights 10pm ET . For the latest from AC360° click here .
Getting rid of assault weapons is `` what we 've really got to work on , '' Bloomberg says . He says he 's encouraging members of Mayors Against Illegal Guns to lobby Congress . Obama 's new measures probably would n't have prevented the Newtown shooting , he says . Still , the New York mayor says , `` fewer guns means you and your children are safer ''