user137658: Is that possible to create new BTC(or any other cryptocurrency) account through free api or kind of?

user137642: It's possible to create an address completely offline.
All addresses exist even if never used in a transaction.
Algorithms needed to generate a new BTC keypair:
 secp256k1
 sha256
 ripemd160
 base58


user13866: 
Is that possible to create new BTC [...] account through free api

The Bitcoin network doesn't have accounts, it is a peer to peer network. To receive and send BTC you only need to install wallet software on your computer or phone. You don't need to create any account.

I need to create address, which could send and receive BTC from another addresses

The normal way to do this would be to download some wallet software to your PC and use that to create addresses.
If you must do it using an API, you can choose wallet software that has an API. For example the Bitcoin Core application software has an API that includes
GetNewAddress

getnewaddress ( "label" "address_type" )
Returns a new Bitcoin address for receiving payments.
If ‘label’ is specified, it is added to the address book so payments received with the address will be associated with ‘label’.


137658: <p>Is that possible to create new BTC(or any other cryptocurrency) account through free api or kind of?</p>
 137642: <p>It's possible to create an address completely offline.<br />
All addresses exist even if never used in a transaction.</p>
<p>Algorithms needed to generate a new BTC keypair:</p>
<pre><code> secp256k1
 sha256
 ripemd160
 base58
</code></pre>
 13866: <blockquote>
<p><strong>Is that possible to create new BTC [...] account through free api</strong></p>
</blockquote>
<p>The Bitcoin network doesn't have accounts, it is a peer to peer network. To receive and send BTC you only need to install wallet software on your computer or phone. You don't need to create any account.</p>
<blockquote>
<p><strong>I need to create address, which could send and receive BTC from another addresses</strong></p>
</blockquote>
<p>The normal way to do this would be to download some <a href="https://bitcoin.org/en/choose-your-wallet" rel="nofollow noreferrer">wallet software</a> to your PC and use that to create addresses.</p>
<p>If you must do it using an API, you can choose wallet software that has an API. For example the <em>Bitcoin Core</em> application software has an API that includes</p>
<p><a href="https://developer.bitcoin.org/reference/rpc/getnewaddress.html" rel="nofollow noreferrer"><code>GetNewAddress</code></a></p>
<blockquote>
<p><code>getnewaddress ( &quot;label&quot; &quot;address_type&quot; )</code></p>
<p>Returns a new Bitcoin address for receiving payments.</p>
<p>If ‘label’ is specified, it is added to the address book so payments received with the address will be associated with ‘label’.</p>
</blockquote>
