Are there any quotes in the play Othello where Iago assures our main protagonist that he is on his side?

There are a number of examples throughout the play in which Iago indicates his support for Othello. He is practicing the art of 'keep your friends close, but keep your enemies closer,' in order to further deceive and manipulate Othello, whom he despises. This is a strategy to further win Othello's trust.

The first example is when he speaks to Othello soon after he and Roderigo had demonized Othello by informing Brabantio in the most slanderously disgusting terms that Othello had abducted his daughter. Iago had then made his way to Othello so that he may think that Iago is there to support him. Iago tells Othello about Brabantio:

Though in the trade of war I have slain men,
Yet do I hold it very stuff o' the conscience
To do no contrived murder: I lack iniquity
Sometimes to do me service: nine or ten times
I had thought to have yerk'd him here under the ribs.

He lies about the fact that Brabantio had so insulted Othello that he felt like killing him, but that he lacks the wickedness to commit such a foul deed. He instead felt like kicking Brabantio under the ribs for defiling Othello's name. He furthermore tells Othello that he had difficulty in restraining himself and wishes to know whether Othello's marriage to Ophelia is secure since Brabantio will make all attempts to have the marriage annulled or use his influence to have Othello punished in some or other way. This is a clear strategy by Iago to win over Othello in proving that he is supportive of him in this matter.

The infernal Iago preys on Othello's sentiments and after creating suspicion in Othello's mind that Cassio and Desdemona might be involved in an illicit liaison, he tells the gullible general:

... now I shall have reason
To show the love and duty that I bear you
With franker spirit: therefore, as I am bound,
Receive it from me. I speak not yet of proof.
Look to your wife; observe her well with Cassio; ...

He actually warns Othello against jealousy when his purpose is actually to ignite this emotion in him. In the extract he tells Othello that he is acting out of love and duty, when he is actually being utterly deceitful. Once again, he seems to be showing his support for Othello in telling him certain truths, which are, in fact, pernicious lies. Iago has, at this point, won Othello's trust completely, judging by the general's monologue in which he refers to Iago in the following terms:

This fellow's of exceeding honesty,
And knows all qualities, with a learned spirit,
Of human dealings.

Later in the play, after Iago once again lies to Othello about Cassio having shared a bed with him. Cassio had, in his sleep, so he claims, passionately kissed him (supposedly believing that he was kissing Desdemona) and mentioned Desdemona's name, cursing the fact that she was married to Othello, Othello is convinced about their adultery. He kneels to make a solemn pledge to take vengeance. Iago uses this opportunity to display his loyalty to Othello. 

Kneels

In the due reverence of a sacred vow
I here engage my words.

IAGO

Do not rise yet.

Kneels

Witness, you ever-burning lights above,
You elements that clip us round about,
Witness that here Iago doth give up
The execution of his wit, hands, heart,
To wrong'd Othello's service! Let him command,
And to obey shall be in me remorse,
What bloody business ever.

He vows to dedicate everything he has to serve Othello who has been wronged. Othello only needs to command and he will perform whatever bloody deed he needs to execute.