An order or a request in indirect speech is expressed by an infinitive:

Direct Speech Indirect Speech
She said to him, “Please, open the window (do not open the window).” She asked him to open the window (not to open the window).
She said to him, “Open the window (do not open the window).” She told him to open the window (not to open the window).
The choice of the verb is determined by the character of the order (request). The verb most commonly used to introduce indirect orders is the verb to tell; the verb to order is frequently used, occasionally also the verb to command.
Direct Speech Indirect Speech
The officer said to the soldiers, “Stop!” The officer commanded the soldiers to stop.
Mr. Bumble said to Oliver, “Bow to the board.” Mr. Bumble ordered Oliver to bow to the board.

The verb to request is used in the official style, chiefly in the Passive Voice.

The verb to request introduces rather a veiled order than a request.

Direct Speech Indirect Speech
The ticket collector said to the passenger, “Produce your ticket.” The ticket collector requested the passenger to produce his ticket.

or:

The passenger was requested to produce his ticket.

Unemotional requests are usually introduced by the verb to ask.
Direct Speech Indirect Speech
He said to a passer-by, “Will you show me the way to the theatre?” He asked a passer-by to show him the way to the theatre.
The verb to beg introduces a request somewhat more emotional.
Direct Speech Indirect Speech
The child said to his mother, “Do take me to the circus!” The child begged his mother to take him to the circus.
Very often, however, it is used in the same meaning as the verb to ask, only it is more polite:
Direct Speech Indirect Speech
He said to the visitor, “Will you walk in?” He begged the visitor to walk in.
Emotional (emphatic) requests are introduced by the verbs to implore to entreat to beseech.
Direct Speech Indirect Speech
Eliza said to the stranger, “Do save my child!” Eliza implored the stranger to save her child.
The verb to urge introduces a request made with great insistence.
Direct Speech Indirect Speech
The mother said to her son, “Do take care of yourself!” The mother urged her son to take care of himself.
As is seen from the above examples, in converting requests beginning with the emphatic do, we use the verbs to implore, to entreat, to beseech, to urge.