Peers have been urged to "respect" voters' decision to leave the EU as they began debating the Brexit bill.
With Prime Minister Theresa May taking the unusual step of sitting in the Lords to watch the opening speeches, Leader of the House Baroness Evans said peers must not "frustrate" Brexit.
But Labour said "reasonable changes" could take place to the bill.
MPs have already backed the proposed law, authorising Mrs May to inform the EU of the UK's intention to leave.
The government does not have a majority in the House of Lords where a record 190 peers are due to speak over two days.
The sitting was extended to midnight on Monday to allow more peers to speak and the debate will continue on Tuesday.
Opposition and crossbench peers are seeking guarantees about the rights of EU citizens in Britain and the role of parliament in scrutinising the process.
Mrs May has said she wants to invoke Article 50 of the 2009 Lisbon Treaty - the formal two-year mechanism by which a state must leave the EU - by the end of March, and the government has warned the House of Lords not to frustrate the process.
The prime minister decided to sit in the Lords chamber itself to listen to the start of the debate. Her official spokesman said this was "in recognition of the importance of this bill as it proceeds through the Lords".
Opening proceedings, Lady Evans said the government had promised to deliver on the result of last year's referendum, in which 51.9% of voters backed Brexit.
She said: "This bill is not about revisiting the debate." She added: "Noble Lords respect the primacy of the elected House and the decision of the British people on 23 June last year."
Lady Evans also said: "This bill is not the place to try and shape the terms of our exit, restrict the government's hand before in enters into complex negotiations or attempt to re-run the referendum."
For Labour, Lords opposition leader Baroness Smith of Basildon said the government would not be given a "blank cheque" and that "if sovereignty is to mean anything, it has to mean parliamentary responsibility".
She promised to make ministers consider "reasonable changes" and this was not "delaying the process" but "part of the process" of Brexit.
But Lord Newby, leader of the Liberal Democrats in the Lords, said the bill could be changed and sent back to the House of Commons for reconsideration, arguing there was a "world of difference between blocking... and seeking to amend it".
The government's approach was "little short of disastrous" and "to sit on our hands in these circumstances is unthinkable and unconscionable", he added.
UKIP's Lord Stevens of Ludgate said the prime minister "should be congratulated" for "honouring" the commitment to leave the EU, following the referendum.
But he told peers it was better to "leave the EU quickly", rather than enter negotiations with member states on a post-Brexit deal.
And Labour peer Lord Howarth of Newport, who backed Brexit, said: "All of us should respect the democratic decision to leave. If we do not, public disaffection from politics will become a crisis. Those who meditate a second referendum are playing with fire."
By Ben Wright, political correspondent
Peers will not block Brexit. But nor are they likely to wave this bill through without asking the Commons to think again about a number of issues.
Peers are certainly keen to have their say in this week's two-day debate.
The committee stage scrutiny - and possible votes - will come the week after.
And with many non-party cross-benchers in the picture the government cannot be certain of defeating all the changes peers will be pushing for. That would mean the Commons could have to consider the bill again.
However, there is no sign the unelected Lords want to go into battle with MPs and the government over Brexit - or meddle with the referendum's mandate.
Labour has said it will not frustrate Theresa May's plan to trigger the start of Brexit by the end of next month.
The government has set aside five days in total to discuss the various stages of the EU (Notification of Withdrawal) Bill - starting with its Second Reading, in which peers debate the general principles of the bill.
The Second Reading debate is due to conclude on Tuesday evening - possibly with a vote, but only if peers break with their usual practice of allowing government legislation through unopposed at this stage.
Although amendments are not voted on at this stage, speeches will be closely watched for signs of the mood of peers on the two key ones of parliament having a "final meaningful vote" on the draft Brexit agreement - and guaranteeing the rights of EU citizens in the UK.
Detailed scrutiny of the bill at committee stage is due to take place on 27 February and 1 March. If the bill is not amended, then it could theoretically be approved by the Lords at Third Reading on 7 March, becoming law shortly afterwards.
If peers do make changes to the bill, it would put them on a collision course with MPs - who overwhelmingly passed the bill unaltered and would be expected to overturn any Lords amendments.
Although the Conservatives have the largest number of peers in the Lords, with 252 members, they are vulnerable to being outvoted if opposition peers - including 202 Labour peers and 102 Lib Dems - join forces.
Much will hinge of the actions of the 178 crossbenchers in the Lords - who are not aligned to any party and do not take a party whip.
Once Article 50 is invoked, there will be up to two years of talks on the terms of the UK's departure and its future relationship with the EU unless all 28 member states agree to extend the deadline.