( 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 . The mayor said he would push for a ban on high-capacity magazines and other gun control measures in the wake of last week's mass shooting at an elementary school in Newtown, 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 ''