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4 May 2015, 21:33 | Updated: 5 May 2015, 12:49
Scottish independence remains the SNP's "ultimate objective", leader Nicola Sturgeon has told supporters.
But she urged committed unionists to join with the SNP "to make Scotland's voice heard" at Westminster during a campaign speech in Dumfries.
Ms Sturgeon attacked critics who say minority government is a recipe for "chaos, gridlock and paralysis of government", pointing out that the SNP's first term in a minority Scottish government was so popular voters handed them a landslide majority in 2011.
Ms Sturgeon also reaffirmed her support for the British monarchy but acknowledged that not everyone in the hall packed largely with SNP activists and supporters would agree with her.
One supporter said: "I've been here since 1968 and even though I am English I am voting SNP, but I don't believe in independence."
Ms Sturgeon replied: "Even though you don't agree with the SNP's ultimate objective of independence, I am delighted that you are voting SNP.
"Indeed, I know many people in this election who voted No in the referendum last year, and who would vote No again if the referendum was tomorrow, who are voting SNP in this election to make Scotland's voice heard.
"I do say to everyone across this country who voted No, take this opportunity, join with us to make sure that as long as we are part of the Westminster system we are part of a greater influence, clout and voice in that system."
She added: "I was the deputy first minister of a minority government for four years.
"If you don't win a majority on polling day, then if you want to be in government and you want to get policies and legislation and budgets through whatever parliament it is that you happen to sit in, then you have to build a majority by working with others.
"If you don't do that as part of a coalition or formal arrangement you have to do that on an issue-by-issue basis, because the alternative is that you don't get your business through the parliament.
"There are those in the Westminster establishment who say that would be dreadful, that would chaos, it would be unstable, it would be gridlock, it would be paralysing the system of government.
"Well, the SNP minority government is proof that none of these things are true.
"We demonstrated that minority government led responsibly and respectfully can be stable, it can be effective, it can be successful.
"The SNP minority government was so successful that voters opted to turn it into a majority government."
Another supporter said: "I understand that you want to abolish the House of Lords because it is unelected and bit old-fashioned, so I was wondering why you don't feel the same way about the British monarchy?"
Ms Sturgeon replied: "Not everybody in this hall will agree with this, but I believe in the Queen as the head of state, that's the position that I argue."
She added: "The House of Lords help write the laws of the land and yet they have no mandate from any elected position, so I don't believe that we should have unelected people making laws, and that's why I think the time for pussyfooting around this is over and it is time to get rid of the House of Lords."
During her speech, Scotland's First Minister repeated her offer to join forces with Labour to "lock the Tories out" of power as she insisted the next government must not simply be made up of the party which has the most MPs in England.
In what has been the closest-fought election for generations, Conservative leader David Cameron and Labour's Ed Miliband are both aiming to win the keys to 10 Downing Street.
But with Thursday's General Election likely to result in another hung parliament, Ms Sturgeon said the SNP - who are tipped to win as many as 50 seats north of the border - could make a "big difference" at Westminster.
Mr Miliband has insisted he will not do any deal with the Scottish nationalists, even if that means forfeiting the chance to be the next prime minister.
Ms Sturgeon said if the Labour leader "is wrong-headed enough to be reject an anti-Tory alliance and let David Cameron back into power '' a strong block of SNP MPs would work ``to protect Scotland from the damage of a Tory government in a way that Labour never has".
The First Minister has said repeatedly if there is an "anti-Tory majority" in the Commons, her party would team up with Labour to prevent Mr Cameron winning a second term - even if his Conservatives win the most seats.
She dismissed suggestions that the largest party needs to form the government to make it legitimate.